Tagged Questions

Representation theory studies (among else) representations of groups by finite matrices. The non-commutative analog of classical Fourier transforms.

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What is the simplest example of the tame representation type?

What is the simplest example of the tame representation type? I tried to find simple example could help me to understand the tame representation type. I know the definition of tame is like: A ...
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If $a\in IBr(G/N)$, then $a\in IBr(G)$? [closed]

If $a\in Irr(G/N)$, then $a\in Irr(G)$. How about replacing Irr by IBr?
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How to compute the number of modular/Brauer characters in a p-blocks of a finite groups, for example $A_5$ or $S_3$?

I do not know how to compute the modular character in a p-block of finite group.I want to know some skills for computing the number of modular characters in a p-block of a finite or some material ...
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Representation of the group of rotations on the space of spherical functions

On a project on how Representation theory can help improve the complexity of shape matching, I couldn't understand this result : If $V$ is the space of spherical functions, consider the ...
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Let $G$ be a Lie group (or more generally a locally compact group), let $N$ be a closed and normal subgroup of $G$ of finite index. Let $H$ be an infinite dimensional complex Hilbert space, and let $\... 0answers 21 views Irreducible representation of$1$-transposition groups I would like to know the theory of irreducible representation of$1$-transposition groups. Could anyone provide me a pointer from where I can proceed? 3answers 54 views Faithful representation of the Heisenberg group I have been trying to solve a problem concerning the Heisenberg Lie group$H$. Show that there does not exist a faithful representation$\rho:H\to\text{GL}(2,\mathbb{R})$. Any ideas about how to ... 0answers 29 views Definition of$k$-transposition group In A monster tale: a review on Borcherds’ proof of monstrous moonshine conjecture, a$k$-transposition group is defined as follows. Recall that a$k$-transposition group$G$is one generated by a ... 0answers 43 views Smoothness of Schubert Variety Consider the Schubert variety$X(s_3s_2s_1s_4s_3s_2)$in$SL_5/P_2$, where$P_2$is the maximal parabolic corresponding to the simple root$\alpha_2$. In one line notation this permutation can be ... 0answers 20 views A$*$-closed algebra of compact operators is completely reducible In page 13 of Lang's$SL_2$there is a proof that for a$*$-closed algebra$\mathscr A$of compact operators on a Hilbert space$H$,$H$is completely reducible. The proof follows by taking the ... 0answers 16 views Is$\pi^1:C_c(G)\rightarrow \operatorname{End}(H)$a homomorphism of the convolution algebra when$G$is not unimodular? Let$G$be a Hausdorff locally compact group and$H$a Banach space. Let$\pi:G\rightarrow \operatorname{GL}(H)$be a representation and define $$\pi^1(\phi)v = \int_G\phi(x)\pi(x)vdx$$ for$v\in H$... 0answers 23 views Special case of Pieri-Rule is there an "elementary" (read: short combinatorial) proof for the rule $$s_\lambda \cdot s_{(1)} = \sum_{\mu} s_{\mu}$$ where$\mu$ranges over all partitions obtained from$\lambda$by adding a ... 0answers 22 views representations of SL_n(R) or SL_n(C) Could someone point me to a reference for the finite dimensional representation theory of$G=SL_n(F)$where$F = \mathbb{R}$or$\mathbb{C}$? In particular, I want to know what this "highest weight" ... 0answers 13 views Irreducible representations of locally compact semigroups What class of semigroups have finite dimensional irreducible representations. For example, If we have a compact groups$G$then every continuous irreducible representation of$G$is finite ... 1answer 36 views Is$\operatorname{Stab}(\lambda)$generated by the simple reflections it contains, for$\lambda\in A_0$? For a finite Weyl group, the stabilizer of an element in the fundamental domain is generated by the simple reflections of the Weyl group that is contains. Does the same still hold for the closure of ... 0answers 40 views Reference Request: Lie Theory For Quantum Field Theory I have encountered the section on non-Abelian gauge theories in Peskin and Schroeder's QFT textbook, and although I am comfortable with the derivation of the Yang-Mills Lagrangian they present, the ... 0answers 23 views (B,N) pair and Steinberg idempotent Let$q=p^f$where$p$is prime and$G$be a finite group with a$(B,N)−$pair ($T=B\cap N$and$W=N/T$), and assume that$B=UT$with$U\triangleleft B$and$U\cap T=1$. Define$$e=\dfrac{1}{[G:U]}\... 0answers 13 views Tannaka Krein duality for finite groups, explicit Tannaka-Krein duality theory says that the natural mapping$G\rightarrow Aut^{\otimes}(F)$(see http://mathoverflow.net/questions/155743/can-one-explain-tannaka-krein-duality-for-a-finite-group-to-a-... 1answer 27 views (B,N) pair and normal subgroup I am trying to prove the following: Let$G$be a finite group with a$(B,N)-$pair and assume that$B=UT$with$U\triangleleft B$and$U\cap T=1$. Let$\widetilde{G}\triangleleft G$such that$U\le \...
The only simple finite groups admitting an irreducible character of degree 3 are $\mathfrak{A}_5$ and $PSL(2,7)$. That seems to be a result coming from Blichfelt's work on $GL(3,\mathbb{C})$, which I ...
I have to find all continuous finite dimensional complex Irreducible and unitary representations of $SO(2)$. I know that every element of $SO (2)$ can be written as $exp(J \theta )$, where $\theta$ ...