All Questions
Tagged with geometric-representation-theory affine-grassmannian
11 questions
3
votes
1
answer
170
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Factoring out an element of a root subgroup to make a conjugation integral
Fix a nonarchimedean local field $L/\mathbb{Q}_p$ with ring of integers $\mathcal{O}$, uniformizer $\varpi$, and residue field $k$. If I take a matrix
$$\begin{pmatrix} a & \varpi b \\ c & d \...
- 12.9k
1
vote
0
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133
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What is Pic of the torus global affine Grassmannian?
Let $T$ be a torus and $X$ a proper smooth curve over characteristic $0$ algebraically closed field $k$.
What is $\text{Pic}(\text{Gr}_{T,X^n})$?
Here $\text{Gr}_{T,X^n}$ is the BD Grassmannian over $...
- 4,713
2
votes
0
answers
124
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Levi quotients of parahorics in loop group
I am looking for some references on Levi quotients of parahorics in $LG = G(\mathbb{C}((t)))$, $G$ being an algebraic group with Weyl group $W$.
I have read that parahoric subgroups of $LG$ are in ...
- 12.9k
2
votes
0
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209
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Error in Proposition 8.7.1 of Pressley–Segal
Let $G$ be a connected, compact Lie group, $T$ a maximal torus. Let $LG$ be the group of smooth (or polynomial) loops and $X=LG/T$ the affine flag variety ($T$ acts say by right multiplication). In ...
- 12.9k
4
votes
0
answers
260
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Stratified fibration property of the "Ran" affine Grassmannian
Let us consider the so-called Ran Grassmannian $Gr_{Ran}$, i.e. the geometric object defined e.g. in [Zhu, An Introduction to the affine Grassmannian and the Geometric Satake equivalence, Definition 3....
- 455
5
votes
1
answer
445
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Drinfeld Sokolov and the semiinfinite flag variety
For a long time I've been confused about Drinfeld Sokolov/BRST reduction/semiinfinite cohomology for affine Lie algebras. Most treatments define it in what to me feels like a fairly ad-hoc way, by ...
- 5,958
1
vote
0
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121
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Coefficient ring of Satake isomorphism
Let $G$ be a split reductive group over local field $F$, $G^L$ be the (complex) Langlands dual group of $G$. Denote $H$ to be the $\mathbb{Z}$-Hecke algebra of $G$, that is the ring of $G(\mathcal{O}...
- 677
8
votes
1
answer
599
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Affine vs Yokonuma
Let $G=GL_n$. Let us start with the Hecke algebra $H_n$. It acts on K(constructible sheaves on $G/B$) by Hecke correpondences and on K(coherent sheaves on $G/B$) by Lusztig's construction [1]. Now we ...
- 206
7
votes
0
answers
168
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Explicit computation for perverse cohomology
To construct the convolution product for two ($G(O)$-equivariant) perverse sheaves $\mathcal{F}, \mathcal{G}$ on affine grassmanian, the first thing we need to compute is $^PH^0(\mathcal{F} \boxtimes^...
- 677
13
votes
0
answers
797
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Borel-Weil-Bott, Langlands and Hitchin
Let $G$ be a compact semi-simple Lie group and $G_\mathbb{C}$ be its complexification. We denote by $B$ a Borel subgroup of $G_\mathbb{C}$.
Given a dominant weight $\lambda$, one can construct a line ...
- 2,273
5
votes
1
answer
605
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Are Strata of the affine Grassmannian total spaces of equivariant vector bundles over flag varieties
This question is closely related to Peter Crooks question.
Strata of the Affine Grassmannian
Let $G$ be a complex reductive group, $\mathcal{K}:= \mathbb{C}((t))$, $\mathcal{O}:= \mathbb{C}[[t]]$ and ...
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