All Questions
Tagged with rt.representation-theory reference-request
823 questions
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Is there a "correct" general setting for the principle: "tensoring any object with a projective object yields another projective"?
Apparently this principle was first formulated for left modules over the group algebra $A=kG$ of a finite group, where $k$ is a field of characteristic $p>0$ dividing $|G|$. (See Exercise 2 on p. ...
CommunityBot
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Embedding into Permutation Representation
Let $\rho$ be irreducible representation of group $G$.
How one can characterize all subgroups $H< G$ such that $\rho$ can be embedded into permutation representation $F^X$, where $X=G/H$.
- 52.9k
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What is known about higher-categorical reconstruction theorems? (reference request)
The answer to my question is almost certainly "not much" — at least, I've asked a few people, and that was their answer. But I'd like to refine this answer, and MathOverflow seems like the best ...
CommunityBot
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Looking for references talking about category of topological vector spaces
It's known that category of topological vector spaces is not abelian but quasi-abelian or exact category. I am looking for the references playing with this category(category theory). All the related ...
- 25.5k
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The finite subgroups of SL(2,C)
Books can be written about the finite subgroups of $\mathrm{SL}(2,\mathbb C)$ (and their immediate family, like the polyhedral groups...) I am about to start writing notes for a short course about ...
CommunityBot
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Applications of classifying thick subcategories
So, relatively recently, Balmer introduced this notion of a spectrum for a tensor triangulated category and used it to prove a generalization of a classification theorem done in several areas of ...
- 13.5k
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Why do Physicists need unitary representation of Kac-Moody algebra?
My advisor mentioned to me that he talked to Witten last summer on representation theory, and Witten told him that unitary representations of Kac-Moody algebra are important to working physicists. But ...
- 33.3k
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Does the Tannaka-Krein theorem come from an equivalence of 2-categories?
Possibly the correct answer to this question is simply a pointer towards some recent literature on Tannaka-Krein-type theorems. The best article I know on the subject is the excellent
André Joyal ...
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How to calculate partition function of a QFT by summing over irreducible representations of the symmetry group?
By definition computing the partition function of a QFT amounts to doing a Feynman Path Integral exactly. At a schematic level I can see why this can become a question of summing/integrating over ...
- 4,577
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Is simple non-holonomic D-module a local concept?
It is well known that we can use the Riemann-Hilbert correspondence to describe holonomic D-modules in terms of a category of perverse sheaves on some variety $X$. And $U|\rightarrow Perv(U)$ is a ...
CommunityBot
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Rallis inner product formula for U(2,2) and U(3)
Victor Tan has a couple of papers on a regularized Siegel-Weil formula for U(2,2) and U(3). The papers I'm talking about are:
"A Regularized Siegel-Weil Formula on U(2,2) and U(3)", Duke, 1998.
"An ...
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Defining a family of rotations with certain properties
Let $d \ge 2$, and consider the sphere $S^{d-1}$ embedded in $\mathbb R^d$. Does there exist a family of rotations $\{\mathcal O_v\}_{v \in S^{d-1}}$ which satisfies:
$\mathcal O_v e_1 = v$, and
$\...
- 44.4k
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Representation theory over Z
In his answer to my question here, Victor Protsak quoted the following result:
Let $C_2$ be a finite cyclic group of order $2$. Then every $\mathbb{Z}[C_2]$ structure on $\mathbb{Z}^n$ is isomorphic ...
CommunityBot
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The geometry of closure of orbit of Borel subgroup in G/B × G/B.
Let $G$ be a reductive group, let $B$ be one of its Borel subgroups, and $T$ be a torus in $B$. $G/B$ is its flag variety. Let $y,w$ be two T-fixed points in $G/B$. Let $\mathcal{O}_{y,w}$ be the $B$-...
- 27.8k
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Several question on Affine Lie algebra
These questions might be elementary for I just started to learn affine Kac-Moody algebra.
It is well known that if we consider finite dimensional Lie algebra, we have the folloing projection:
$R(\...
CommunityBot
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What is Extreme/Extremal vector according to some weights
I know this might be a very elementary question. But I could not find the original definition of Extreme(or Extremal)vectors of some weights $\lambda$(fixed the $w\in W$,where $W$ is Weyl group)
I am ...
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14
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How many ways are there to prove flag variety is a projective variety?
I am looking for references talking about different ways to prove flag variety $G/B$ is projective variety. Now I have some in mind:
There is a proof in Humphreys Linear algebraic groups, he first ...
- 5,515
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2
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Reference request: A theorem by S. Garrison
A theorem by S. Garrison states that if $G$ is a finite solvable group and $|cd(G)| = 4$ then $dl(G)\leq |cd(G)|$ (the Taketa inequality, which is conjectured to hold for all finite solvable groups). ...
- 10.7k
4
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What is the relationship between representations of Lie algebra and Weyl algebra?
Is there any paper talking about the relationship of representation of finite dimensional Lie algebra and Weyl algebra? Can we construct representations of Lie algebra from representations of Weyl ...
CommunityBot
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References for Lie superalgebras
Does anybody know good references to learn about Lie superalgebras? I started with Howe's "Remarks on classical invariant theory", which contains a study of osp(m,2n), and now I am reading Kac's '77 ...
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An arithmetic highest weight theory?
I apologize if these questions seem naive or loaded.
Is there an analogous theory of highest weights for irreducible finite-dimensional representations of Lie algebras of algebraic group (or perhaps ...
- 7,108
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Reference on a result on representation of moderate growth
Let G be a real reductive group, and P any parabolic subgroup. In the paper 'Canonical extensions of Harish-Chandra modules to representations of $G$' by Casselman, a result says that if we begin with ...
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Complexes of representations with complementary central charges
This is another question asking for references. There is an important phenomenon of correspondence between (complexes of) representations of infinite-dimensional Lie algebras with the complementary ...
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