# Tagged Questions

**19**

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**2**answers

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### Current Status on Langlands Program

The Langlands Program was launched almost fifty years ago, and progress has been made gradually, much of it hard earned. Langlands himself wrote a survey on the functoriality conjecture in 1997, Where ...

**0**

votes

**1**answer

201 views

### Reference on Casselman-Shalika formula for GL(n) and PGL(n)?

I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.

**1**

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229 views

### Complex Finite Dimensional Representation of GL(N,C)

What are all the complex finite dimensional linear representation of $GL(N,\mathbb{C})$?
We already know all the complex finite dimensional linear representation of SU(N).

**1**

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**2**answers

188 views

### Symmetric and Exterior products of sl(n,C)-module

Let M be the $sl(n,C)$-representation of the inclusion $sl(n,C)\hookrightarrow gl(n,C)$.
Let q be a symbol.
$f(q)=1-M q + \wedge^2Mq^2-...+(-1)^n\wedge^nMq^n$
$g(q)=\sum_{i=0}^\infty Sym^iM \; q^i$
...

**2**

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**0**answers

197 views

### Local counterpart of the NON-Hitchin Hecke eigen-sheaves ?

Insight of Beilinson and Drinfeld at early 90-ies - that Hitchin's D-modules are Hecke eigen-D-modules. However they are NOT all Hecke-eigensmodules and actually they are only the half-dimensional ...

**11**

votes

**1**answer

940 views

### What is the relation between L. Lafforgue and Frenkel-Gaitsgory-Vilonen results on Langlands correspondence ?

What is the relation between Lafforgue's result on Langlands
and Frenkel-Gaitsgory-Vilonen ? ( http://arxiv.org/abs/math/0012255 , http://arxiv.org/abs/math/0204081 )
Does one imply other ? If not ...

**1**

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**0**answers

237 views

### Orbit stratification of semi infinite flag manifold?

Denote semi infinite flag manifold by $Fl_{\infty/2}=G((t))/N_-((t))H[[t]]$, denote $B_-((t))=N_-((t))H[[t]]$
from the book of Frenkel and Benzvi" Vertex algebras and algebraic curves", They take ...

**1**

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**2**answers

551 views

### Opers, connections

My questions here are from my attempt at trying to understand the definition on pg 15 in [FG2]-"Local Geometric Langlands Correspondence & Affine Kac-Moody Algebras" ...

**5**

votes

**1**answer

621 views

### Fiber functor of category of D-module on affine Grassmannian.

Geometric Satake correspondence allows us to construct Langlands dual group in a canonical way. In Mirkovic-Vilonen's paper, they prove that category of spherical perverse sheaves is an commutative ...

**5**

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**2**answers

707 views

### A question on group action on categories

Let $Gr$ be the affine Grassmannian of $G=G((t))/G[[t]]$, and let $Perv(Gr)$ be the category of perverse sheaves on $Gr$. We have action of $G((t))$ on the left-hand side of $Perv(Gr)$, also we have ...

**40**

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**1**answer

3k views

### Double affine Hecke algebras and mainstream mathematics

This is something of a followup to the question "Kapranov's analogies", where a connection between Cherednik's double affine Hecke algebras (DAHA's) and Geometric Langlands program was mentioned.
I ...

**4**

votes

**1**answer

624 views

### Explanation for Satake correspondence

Some time ago I was told there's an interesting classical Satake correspondence which I will write as
$$[\mathop{\mathrm{disk}} \Rightarrow G] \\,\backslash\\, [\mathop{\mathrm{disk}^\times} ...

**5**

votes

**0**answers

247 views

### Real representations of G = those of Langlands dual and maps of a cylinder

There is a result about the real representations of a simple Lie group $G$ which is known as Soergel conjecture or Vogan duality. We'll focus on the formulation that for a fixed character of $G$
...

**28**

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**1**answer

5k views

### Consequences of Geometric Langlands

So, lots of people work on the Geometric Langlands Conjecture, and there have been a few questions around here on it (admittedly, several of them mine). So here's another one, tagged community wiki ...