The Geometric Langlands correspondence introduced by Drinfeld and Laumon conjectures a 1 to 1 correspondence between (A) local systems on a projective smooth curve over a field a …

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

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}^\in …

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).

In geometric Langlands, one looks at correspondences of the form $$ Bun_n(X) \leftarrow Hecke \rightarrow X\times Bun_n(X)$$ and calls a sheaf on the lefthand space Hecke eigens …

Geometric Langlands for Kac-Moody, non-critial level? After Beilinson 2006, Frenkel 2007 (Loop groups)

Q1: Here, on pg $103$, the stack $\text{LocSys}_G(X)$ is defined (for an affine algebraic group $G$, a fixed DG scheme $X$, and a test scheme $S \in \textbf{DGSch}$): $Maps(S, Loc …

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 im …

Can someone explain, explicitly, how to, given a reductive complex algebraic group construct the Langlands dual group? I know it is a group with the cocharacters of G as its charac …

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 cu …

What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker? (So I do not mean …

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 …

I'm currently working through Frenkel's beautiful paper: http://arxiv.org/PS_cache/hep-th/pdf/0512/0512172v1.pdf. I'm looking for a good example of a projective curve to get my h …

For some time I've been intrigued by the fact that the splitting of a complex vector bundle $V$ over a manifold $B$ into line bundles via successive projectivizations "mirrors" the …

Considering the Arthur trace formula, why are the sort of convolution operators, whose "normalized traces" are given in geometric terms and spectral terms, actually able to disting …