All Questions
Tagged with geometric-representation-theory at.algebraic-topology
7 questions
7
votes
0
answers
160
views
comparison of polynomial loop group and smooth loop group
I have a question about Section 8.6 of Pressley-Segal's Loop groups book. Let $G$ be a compact, connected Lie group. Proposition 8.6.6 concerns the comparison of homotopy type between its polynomial ...
- 959
19
votes
0
answers
661
views
Homotopy type of the affine Grassmannian and of the Beilinson-Drinfeld Grassmannian
The affine Grassmannian of a complex reductive group $G$ (for simplicity one can assume $G=GL_n$) admits the structure of a complex topological space. More precisely, the functor $$X\mapsto |X^{an}|$$ ...
- 455
12
votes
2
answers
887
views
Representation viewpoint on Chern–Weil (cohomology computations done with rep theory?)
$\DeclareMathOperator\Sym{Sym}$Let $G$ be a compact lie group. Chern–Weil theory tells us that there's a homomorphism:
$$H^{*}(BG;\mathbb{R}) \to (\Sym^{\bullet} \mathfrak{g^*})^G$$
which in our case ...
- 7,789
8
votes
2
answers
2k
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Global Affine Flag Variety and Affine Flag Variety
There is a construction of a global affine flag variety over $\mathbb{A}^1$ (or another curve) $Fl_{\mathbb{A}_1}$ such that each fiber above $\epsilon \neq 0$ is isomorphic to a direct product of the ...
- 1,719
11
votes
1
answer
1k
views
Characteristic Classes in Geometric Representation Theory
Geometric respectively topological methods are widely applied in representation theory. As far as I know mainly cohomological methods are used.
I wonder if there are concrete applications of the ...
- 2,554
2
votes
1
answer
687
views
Derived Push-Forward of Morphism of Perverse Sheaves and Translation Functors
I hope this question is not too vague.
Let $G$ be a complex reductive group, $B$ a Borel subgroup of $G$, and $P$ a parabolic containing $B$.
Denote by $\pi:G/B\to G/P$ the canonical map. Consider ...
- 2,554
6
votes
0
answers
532
views
Can one calculate Ext's between microlocalized perverse sheaves/D-modules using topology?
So, I know one really good technique for calculating Ext's between perverse sheaves/D-modules using topology: the convolution algebra formalism, worked out in great detail in the book of Chriss and ...
- 44.7k