# Questions tagged [reference-request]

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

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### Connections between linear representations and permutation representations

A finite group $\Gamma$ might be represented by a linear transformation $$\rho : \Gamma\to\mathrm{GL}(\Bbb R^d),$$ or by permutations $$\phi :\Gamma\to\mathrm{Sym}(n).$$ Of course, latter ones can ...
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### Reference request: book on stochastic calculus (not finance)

I am looking at fractional Gaussian/Brownian noise from a signal theoretic and engineering point of view. In particular, I am looking at the math behind what defines these noise processes and what ...
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### What is a name for co-Sobczyk Banach spaces?

Definition. Let us define a Banach space $X$ to be co-Sobczyk if every linear bounded operator $T:Z\to c_0$ defined on a separable subspace $Z$ of $X$ extends to a bounded operator $\bar T:X\to c_0$. ...
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### Concrete example to illustrate the theory about blocks of groups with cyclic defect groups

I'd like to to have a concrete example to illustrate the theory about blocks of groups with cyclic defect groups. Thus, I am looking for a finite group $G$ and a prime $p$ dividing $|G|$ satisfying ...
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### Wellposedness of semilinear wave equation with discontinuous source

Where can I find existence and uniqueness results for semilinear wave equations with discontinuous, i.e. $$\partial^2_{tt} u - \Delta u = f(u), \quad t >0, \ x \in \Omega$$ where $f$ is ...
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### Cotangent Complex in Analytic Category

I am looking for a reference which develops the theory of the cotangent complex for complex analytic spaces. I need this to justify some computations I did assuming some formal properties which hold ...
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### Analytic sets are rectifiable

I am looking for a reference on the statement that real analytic sets (i.e. sets in the form $u^{-1}(0)$ where $0\not\equiv u:E\subset \mathbb{R}^n\to \mathbb{R}$ is analytic, or finite intersections ...
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### Holomorphic versus algebraic $\mathbb C^*$-actions

I believe that the following is true: Statement. A holomorphic $\mathbb C^*$-action on a complex projective manifold is algebraic if and only if it has a fixed point. Where can I find a proof of ...
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### The category of complexes over a dg-algebra is Grothendieck (it has a generator)

Let $A$ be a dg-algebra over some commutative ring $k$. We have an abelian category $\mathrm{C}(A)$ of (right) $A$-dg-modules. I've read in a few sources that $\mathrm{C}(A)$ is a Grothendieck abelian ...
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### Bridging between Rosethal Inequalities and log convex tails

Let $X_1,\ldots,X_n$ be independent with $\mathbf{E}[X_i] = 0$ and $\mathbf{E}[|X_i|^t] < \infty$ for some $t \ge 2$. Write $\|X\|_p = (E|X|^p)^{1/p}$. Then we have the classical "Rosenthal-type ...
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### Denominator identity for Lie superalgebras

Let $\mathfrak g$ be a basic classic simple Lie superalgebra. Fix a maximal isotropic subset $S \subset \Delta$ and choose a set of simple roots $\Pi$ containing $S$. Let $R$ be the Weyl ...
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### Monadic second-order theories of the reals

I’m looking for a survey of monadic second-order theories of the reals. I’m starting from a 1985 survey by Gurevich which says (p 505) that true arithmetic can be reduced to “the monadic theory of ...
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### Do we know what the impulse to “introduce” the Jordan canonical form was?

Mo-ers, Do you know how it was that the study of the Jordan canonical form began? There are certain things that may be said once one has thought about the matter: for instance, one can say that the ...
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### Dynkin diagram of Basic classical simple Lie superalgebras

Let $\mathfrak g = \mathfrak g_0 \oplus \mathfrak g_1$ be a basic classical simple Lie superalgebra with the root system $\Delta = \Delta_0 \cup \Delta_1$ and Dynkin diagram $\Gamma$. It is well-known ...
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### Reference request: When is the variance in the central limit theorem for Markov chains positive?

I'm looking for a reference which gives sufficient conditions for the variance to be positive in the central limit theorem for Markov chains (cf https://en.wikipedia.org/wiki/...