Tagged Questions
This tag is used if a reference is needed in a paper or textbook on a specific result.
0
votes
0answers
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 ...
1
vote
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 ...
1
vote
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
votes
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
$$
(A,B) \cdot (M_1, \ldots, M_m) ...
6
votes
0answers
60 views
When were bordered Heegaard Floer homology's DA bimodules invented?
This is less of a strictly mathematical question and more of a reference request.
In their paper "Bordered Heegaard Floer Homology (http://arxiv.org/pdf/0810.0687.pdf)," Lipshitz-Ozsvath-Thurston ...
3
votes
1answer
214 views
What year was Hechler forcing created?
Hechler forcing is described on page 278, Jech.
Does anyone know when Hechler forcing was first used in a publication?
4
votes
0answers
119 views
Universal property of module categories over monads
Let $T$ be a monad on a cocomplete category $\mathcal{C}$. Let's assume that $T$ preserves reflexive coequalizers (or something weaker?). Then the category of $T$-modules $\mathsf{Mod}(T)$ is ...
3
votes
1answer
70 views
Extremal graph theory for directed graphs
In extremal graph theory, there are results such as
$$t(C_4,G)\geq t(K_2,G)^4,$$
where $G$ is an undirected graph, $C_4$ is a cycle graph on 4 nodes, $K_2$ is a complete graph of $2$ nodes, and ...
1
vote
0answers
61 views
Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?
In many applications, it is possible to derive an explicit expression for the
Fourier transform of a random variable $X$
$$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$
...
3
votes
0answers
41 views
Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities
In his paper “Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche” I. Schur has stated that Frobenius has communicated to him a simple direct proof of his finite version of the ...
0
votes
0answers
38 views
First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric
This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions.
We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...
5
votes
0answers
66 views
Comparison of K-groups of (affine) singular schemes with K'=G-groups
It is well known that Quillen K-theory coincides with $K'=G$-theory for regular schemes, and can be distinct from it for singular ones. Are there any methods for studying this distinctions? In ...
0
votes
0answers
52 views
Cancellations in products of two elements of a hyperbolic group
Let $G$ be a non-abelian free group with the standard generating set and the corresponding word metric. If we take two elements $g,h\in G$ and compute their product $gh$, some letters might cancel, ...
1
vote
1answer
91 views
On the geometry of roots of a sum of complex linear fractions
I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form
$$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$
where the $a_j$'s are nonzero complex ...
1
vote
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 ...
1
vote
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$ ...
0
votes
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
votes
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 ...
2
votes
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 ...
5
votes
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 ...
0
votes
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
votes
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 ...
3
votes
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.
1
vote
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 ...
1
vote
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\{ ...
-3
votes
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?
6
votes
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. ...
9
votes
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 ...
0
votes
0answers
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
votes
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
votes
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 < ...
5
votes
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 ...
2
votes
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
votes
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 ...
7
votes
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) ...
3
votes
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
votes
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
votes
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
votes
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
votes
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 ...
4
votes
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 ...
0
votes
0answers
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
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
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 ...
