All Questions
Tagged with sheaf-theory rt.representation-theory
9 questions
7
votes
1
answer
490
views
Equivariant perverse sheaves and orbit stratification
Let $X$ be a complex algebraic variety with an action of a connected algebraic group $G$.
The forgetful functor from the category of $G$-equivariant perverse sheaves on $X$ to the category of perverse ...
- 3,446
7
votes
0
answers
217
views
Correspondence between Verma module morphisms and invariant differential operators - is it exact?
For a (complex, connected, simply connected, simple) Lie group $G$, a parabolic subgroup $P \subseteq G$, and a $\mathfrak g$-integral $\mathfrak p$-dominant weight $\lambda$, we can construct ...
- 1,368
11
votes
1
answer
812
views
Understanding the purely formal part of the sheaf theoretic (cohomological) framework for representation theory
By now I have the impression that many statements in representation theory can be phrased a lot more elegantly using cohomological language. Therefore I'm trying to understand a bit better the sheaf ...
- 7,789
1
vote
1
answer
690
views
Beilinson-Bernstein localization: $\mathfrak{g}$ action on $G$-equivariant sheaf
I have a few elementary questions related to Beilinson-Bernstein localization.
Let $G$ be a semisimple algebraic group over $\mathbb{C}$ with Lie algebra $\mathfrak{g}$. Consider the setup of ...
- 174
2
votes
0
answers
180
views
on geometric Satake and functions
Let $G(F)/G(O)$ the affine grassmanian with $F=k((t))$ where $k$ is a finite field.
For $\lambda$ a dominant cocharacter, we have by Cartan decomposition the schubert strata $\overline{Gr^{\lambda}}$....
- 3,472
5
votes
0
answers
564
views
About an argument in `Koszul duality patterns in representation theory' by Beilinson-Ginzburg-Soergel.
I am trying to understand Proposition 3.4.2 in `Koszul duality patterns in representation theory' by Beilinson-Ginzburg-Soergel [BGS]. A copy of the paper can be found at http://home.mathematik.uni-...
- 1,595
19
votes
2
answers
3k
views
Explaining Mukai-Fourier transforms physically
A core concept in mathematics, engineering, and physics is the Fourier Transform (FT) and its many variants (Generalized Fourier Series, Green's Function, Pontryagin duality).
The basic algorithm is ...
- 10.5k
5
votes
2
answers
987
views
The equivalence of category of equivariant sheaves on principal bundle and category of sheaves on base space
Let $\pi:P\to B$ is a $G$-principal bundle, which means $G$ acts on $P$ freely and $\pi$ is a locally trivial fibration. Here is a well-known theorem:
THeorem: The inverse image functor $\pi^{*}$ ...
- 1,457
21
votes
3
answers
2k
views
Is there a "categorical" description of Grothendieck's algebra of differential operators?
First, pick a commutative ring $k$ as the "ground field". Everything I say will be $k$-linear, e.g. "algebra" means "unital associative algebra over $k$". Then recall the following construction due ...
- 54.6k