# Tagged Questions

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### Reference Request: Characters of Finite General Linear Groups

I've been looking at J.A. Green's article The Characters of Finite General Linear Groups and it seems that Green in this article comes up with a way of calculating all irreducible characters of a ...
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### Representation theory over $\mathbb{Q}$

I am looking for books or papers which tell me something about representation theory of finite groups over $\mathbb{Q}$ (or finite extensions thereof which are not splitting fields of the group ...
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### Why does the universal cover of $GL^+_n$ not admit finite-dimensional representations?

Let $GL^+_n \subset \mathbb{R}^{n \times n}$ be the subgroup of real matrices with positive determinant and $\widetilde{GL}^+_n$ be its universal cover. Why does $\widetilde{GL}^+_n$ not admit ...
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### Reference for Weyl Character Formula

I am reading Lie algebra book by James E.Humphreys. This book giving enough discussion about Weyl Character Formula and its proof, still I would like to know what are the other books or lecture notes ...
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### History of representation theory

For a student's journal I want to write a short article about history and importance (applications) of representation theory. Are there some accesible literature about this?
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### representations into $\mathfrak{sl}(n,\mathbb{C})$

in Borel/Ji "Compactification of symmetric and locally symmetric spaces" the standard Satake compactification is constructed and general Satake compactifications are realized via an embedding into the ...
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### What is $\mathfrak{gl}(\infty)$

As title says, I know what is $\mathfrak{gl}(n,\mathbb{C})$, but what is $\mathfrak{gl}(\infty)$? Where can I find good reference for this?
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### Eigenbundle decomposition

Let $G$ be a finite cyclic group and $X$ a smooth manifold equipped with a trivial $G$-action. It is known that we can decompose every $G$-equivariant vector bundle with respect to the action: ...
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### Representation Theory book other than Fulton's

Fulton/Harris's book on representation theory seems to be the "definitive" introductory text on the subject. But is there perhaps a lower level introduction to the subject? Most of the very first ...
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### Finding Idempotents?

I was wondering if there is a method for finding primitive idempotents of a finite dimensional algebra (over a field)? or in other words is there any way to build the complete set of primitive ...
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### Reference request for studying Lie group & Lie algebra representations

I am learning representation theory of Lie groups & Lie algebras from the book by Brian Hall. Unfortunately, this does not discuss infinite dimensional representations. Which books should I study ...
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### reference request: proof that group characters are a basis for $L^2$

I know the following must be very standard, but I haven't found it in any of the functional analysis books to which I have access. Do you know where I can find a self-contained proof?: If $G$ is a ...
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### Research paper in harmonic analysis that can be read in parallel to studying the subject.

In my idle hours I started to learn some math I touched only superficially in academia in former times. Among others I am working through the books of A. Deitmar on harmonic analysis. I've almost ...