This tag is used if a reference is needed in a paper or textbook on a specific result.

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32 views

Jacobian change of basis matrix for different dimensions

I am considering a real Lie group $G$ acting transitively on an open set $U$ in a real Euclidean space of lower dimension. Given a smooth, compactly supported function $f: G \rightarrow \mathbb{R}$, I ...
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0answers
55 views

Could one recover the relative K-theory from the quotient derived category?

Let $A\to B$ be a full embedding of exact categories that induces an embedding $D^b(A)\to D^b(B)$. My question is: what can one say about the relation of the homotopy cofibre $K(A)\to K(B)$ (the ...
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0answers
58 views

K-theory of ringed spaces (including henselian and formal schemes); excision and Mayer-Vietoris

Given a ringed topological space $S$ one can easily define its K and K'-theory as the K-theories of the categories of locally free sheaves and of the category of coherent sheaves on it, respectively. ...
4
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0answers
72 views

$SL(n) \times SL(n)$-invariants of $m$-tuples of matrices

I work over field of complex numbers. Let $G=SL(n) \times SL(n)$, and $(A,B) \in G$ acts on $m$-tuples of matrices $M_{n \times n}(\mathbb{C})^{\oplus m}$ as follows $$ (A,B) \cdot (M_1, \ldots, M_m) ...
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60 views

When were bordered Heegaard Floer homology's DA bimodules invented?

This is less of a strictly mathematical question and more of a reference request. In their paper "Bordered Heegaard Floer Homology (http://arxiv.org/pdf/0810.0687.pdf)," Lipshitz-Ozsvath-Thurston ...
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1answer
214 views

What year was Hechler forcing created?

Hechler forcing is described on page 278, Jech. Does anyone know when Hechler forcing was first used in a publication?
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0answers
119 views

Universal property of module categories over monads

Let $T$ be a monad on a cocomplete category $\mathcal{C}$. Let's assume that $T$ preserves reflexive coequalizers (or something weaker?). Then the category of $T$-modules $\mathsf{Mod}(T)$ is ...
3
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1answer
70 views

Extremal graph theory for directed graphs

In extremal graph theory, there are results such as $$t(C_4,G)\geq t(K_2,G)^4,$$ where $G$ is an undirected graph, $C_4$ is a cycle graph on 4 nodes, $K_2$ is a complete graph of $2$ nodes, and ...
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0answers
61 views

Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?

In many applications, it is possible to derive an explicit expression for the Fourier transform of a random variable $X$ $$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$ ...
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41 views

Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities

In his paper “Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche” I. Schur has stated that Frobenius has communicated to him a simple direct proof of his finite version of the ...
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0answers
38 views

First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions. We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...
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0answers
66 views

Comparison of K-groups of (affine) singular schemes with K'=G-groups

It is well known that Quillen K-theory coincides with $K'=G$-theory for regular schemes, and can be distinct from it for singular ones. Are there any methods for studying this distinctions? In ...
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0answers
52 views

Cancellations in products of two elements of a hyperbolic group

Let $G$ be a non-abelian free group with the standard generating set and the corresponding word metric. If we take two elements $g,h\in G$ and compute their product $gh$, some letters might cancel, ...
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1answer
91 views

On the geometry of roots of a sum of complex linear fractions

I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form $$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$ where the $a_j$'s are nonzero complex ...
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0answers
60 views

Reference Request: Algebraic Serre's Duality Theorem for Curves

Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne ...
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4answers
173 views

Bruhat order and Schubert cycles

I am looking for a good (textbook) reference for the basic fact (due to Chevalley) that for every semisimple Lie group $G$ (without compact factors) with Weyl group $W$, the Bruhat order on $W$ ...
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0answers
56 views

Reference request: Heat kernel regularity near the boundary

Let $D$ be a domain in $\mathbb{R^d}$ and $p(t,x,y)$ be the heat kernel of $D$ (for the Dirichlet problem). I was told that if the boundary of $D$ is real-analytic, then the function $y\mapsto ...
3
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1answer
158 views

References for von Neumann Algebras

I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in ...
0
votes
1answer
63 views

reference request: trace/lifting operator for $L^{\infty}$ data in bounded $\Omega\subset R^d$

I know the answer to my question must be somewhere in the literature. Probably in [Adams-Fournier], [Dautray-Lions] or something alike, but I don't have access to a library right now so I'll ask ...
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2answers
144 views

If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?

Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post). Basically following some ideas of W. Lawvere (but not his ...
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0answers
356 views

Different approaches to the multiverse of sets

There are some different approaches to the multiverse of sets, in particular: 1) The approach by Woodin, 2) The approach by Sy Friedman, ..., 3) The approach by Hamkins. I wonder to know if ...
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1answer
59 views

Laplacian matrix of a graph with negative weights

I am trying to calculate the Laplacian and Adjacency matrix of a graphs for positive and negative weights. If a graph be simple with only non-negative weight it is easier. But in my graph I have some ...
2
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0answers
57 views

Genericity of maps which are transverse when restricted to a submanifold

Let $M$ and $N$ be smooth manifolds, and $A\subset M$, $B\subset N$ be smooth embedded submanifolds. I am looking for a reference for a theorem on the following lines: The set of smooth maps $h\in ...
4
votes
2answers
214 views

Reference for $p$-adic Hodge theory with coefficients

Let $K$ be a $p$-adic field and $L$ be a finite or infinite extension (maybe algebraic ?) of $\mathbb{Q}_p$. Is there a reference for $p$-Hodge theory for representations $\rho : Gal_K \rightarrow ...
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0answers
278 views

Continued fraction representation of Zeta

A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any. I found this at arxiv, but it doesn't apply to Zeta.
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0answers
51 views

Bases of a matroid such that their complement is an independent set

Let $M$ be some matroid on $[n]$ with set of bases $\mathcal{B}$. I am interested in the subset $\mathcal{B}' \subseteq \mathcal{B}$ of bases $b \in \mathcal{B}$ with the property that $[n] \setminus ...
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2answers
251 views

How to prove $\mathop {\lim }\limits_{x \to \infty } \sum\limits_{{f_x}(p) = 1} {\frac{1}{p}} = \ln 2$ for $p \le x$?

Let ${f_x}(m) = \sum\limits_{\left. p \right|m} {{f_x}(p)}$ be a strongly additive function on positive integer number $m$, where $p$ is a prime number. Set $${f_x}(p) = \left\{ ...
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0answers
55 views

Reference request for the irreducibility of the adjoint representation of $SU(n)$ [closed]

I would like to quote the following fact: "The adjoint representation of $SU_n$ on its Lie algebra $\mathfrak{su}_n$ is irreducible." Do you know any standard reference?
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2answers
176 views

Literature on “real” $C^*$-algebras

I am trying to get a better understanding of "real" $C^*$-algebras. I encountered them in the paper D. Voiculescu, Dual algebraic structures, J. Operator Theory 17(1987), 85-98, which cites G.G. ...
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1answer
292 views

Applications of SCH outside of set theory

Recall that the Singular Cardinals Hypothesis (SCH) says that if $\kappa$ is a singular cardinal and $2^{cf(\kappa)}<\kappa,$ then $\kappa^{cf(\kappa)}=\kappa^+.$ Clearly it has many applications ...
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67 views

Exposition of the Calabi complex

I am interested in a complex derived by Eugenio Calabi in his article "On compact Riemannian manifolds with constant curvature". The complex is referenced as "Calabi complex" in various citing ...
4
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1answer
95 views

Generalized permutahedron and random polytopes

The Birkhoff polytope $B_n$ is defined as the convex hull of the set of permutation matrices, which gives us the set of doubly stochastic matrices. A concept which is intimately related is that of the ...
3
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1answer
91 views

Embedding a linearly ordered free monoid into a linearly ordered group

A linearly ordered (shortly, l.o.) monoid is a triple $\mathbb M = (M, \cdot, \le)$ for which $(M, \cdot)$ is a (multiplicatively written) monoid and $\le$ is a total order on $M$ such that $xy < ...
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2answers
325 views

Looking for paper: The Cauchy integral by M. Privalov

I am looking for a paper titled The Cauchy integral by M. Privalov (Saratov, 1919). The paper is written in Russian. It is being cited (for instance) by A. Kolmogorov in the paper Sur les fonctions ...
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4answers
332 views

Reference for Kronecker-Weyl theorem in full generality

The Kronecker-Weyl theorem asserts the following: fix real numbers $\theta_1,\dots,\theta_d$, and consider the infinite ray $t(\theta_1,\dots,\theta_d)$ $(t\in\Bbb R)$ inside the $d$-dimensional torus ...
2
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1answer
240 views

Looking for paper: Weil's original 1952 “Sur les formules explicites de la théorie des nombres premiers”

I am looking for a source (preferably online) for Weil's original 1952 paper on the explicit formula. I am aware of an english translation available here, but would like to have access to the original ...
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4answers
448 views

Conjugation Quandles and… “Quandle-Groups”? From quandles to Groups

This question is already asked MathSE A quandle $(Q,*,/ )$ is a idempotent right-distributive and right invertible structure. 1) $a*a=a$ 2) $(a*b)*c=(a*c)*(b*c)$ 3) $(a*b) ...
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0answers
81 views

Bicategorical limits with parameters

(This question was asked in http://math.stackexchange.com/questions/741334/bicategorical-limits-with-parameters with no answer.) Let $F(-,-)\colon \mathcal{A}\times \mathcal{B}\to \mathcal{C}$ be a ...
2
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1answer
156 views

Classical theory for the incompressible Euler equation (reference request)

I have recently been interested in the incompressible Euler equation, but since I am new to the topic, I would like to inquire what are the standard sources/references (for self-study) regarding the ...
7
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0answers
99 views

Algebraic construction of the modular representation of $\mathrm{SL}_2(\hat{\mathbf Z})$

The answer to this question is probably to be found in the theory of automorphic forms, but (I don't know much about it and consequently) after some tries, I did not catch it. Thus I'd be grateful if ...
4
votes
1answer
109 views

Graph presentation of Lexicographic shifts

Consider a finite alphabet $\{0,1, \ldots, n-1\}$. Let $\Sigma_n = \mathop{\prod}\limits_{j=1}^{\infty}\{0, \ldots n-1\}$ be the set of infinite one sided sequences and $\prec$ the lexicographic ...
3
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1answer
142 views

Understanding a particular approximation for Stirling's number of the second kind

I noticed and employed (without a problem) an approximation for Stirling's number of the second kind found on Wikipedia (http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind), in ...
3
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1answer
51 views

Reference request: results on the asymptotic distribution of singular values related to a random orthogonal matrix

Let $Q$ be a random variable taking as its values the set of $n \times k$ real matrices with orthogonal columns, and whose distribution is the Haar measure on the Stiefel manifold $O(n)/O(n-k)$. This ...
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0answers
112 views

Is there a version of Serre's modularity conjecture for projective representations?

Serre's modularity conjecture asserts that a continuous odd irreducible representation $$\overline{\rho} : G_\mathbb{Q} \rightarrow \mathrm{GL}_2(\mathbb{F}_q)$$ must be modular, in the sense that ...
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46 views

Discrete Fourier tranform on $L^2(\mathbb{R})$

I'm studying on the following construction: For $\lambda\in\mathbb{R}$, denote $$Y_{\lambda}=\left\{g\in L^{2,loc}(\mathbb{R})\,:\,g(t+2\pi)=e^{2\pi i\lambda}g(t)\right\}$$ We give to $Y_{\lambda}$ ...
0
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0answers
114 views

singularities and zeros of series and reverse problem [closed]

Given a series $$S=\sum_{n=1}^{\infty}a_n x^n,a_n\in \mathbb{N}$$ we know that it may have zeros,poles,branch points or natural boundary.Reversely,given it's zeros,poles,branch points or natural ...
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0answers
82 views

Ref request: If an affine subspace $V$ of $\mathbb R^n$ meets an $n$-dimensional polytope $P$, then it meets $P$ in a face of dimension $\le n-\dim V$

Let $P$ and $V$ be, respectively, a bounded full-dimensional polytope and an $m$-dimensional affine subspace of $\mathbb R^n$, and assume $P \cap V$ is non-empty. Q1. Could you provide me with a ...
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5answers
375 views

Character table of $S_7$

Is there any reference where I can find the character table of the symmetric group $S_7$? A simple search in google gave me a GAP program that computes the character table, but I don't understand the ...
4
votes
3answers
322 views

Systematic brute-force searches for counterexamples

This is getting nowhere on math.stackexchange.com, so I'm putting it here. Gödel's completeness theorem says that for every statement in first-order predicate calculus with equality, there is either ...
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2answers
200 views

Lattices in general totally disconnected locally compact groups

Besides automorphism groups of trees and buildings, I was wondering if the lattices in general totally disconnected locally compact groups have been studied in the literature? I appreciate if you ...