I am wondering if there is a good motivation for geometric representation theory from within the questions of classical representation theory. In other words, I'd be curious to se …

I'm trying to understand the Borel--Weil theorem at the moment (not the whole Bott--Borel--Weil theorem as has been asked elsewhere). However, I am having a little difficulty find …

Let $\mathcal{O}_0$ be the principal block of the BGG category $\mathcal{O}$ for a finite dimensional simple Lie algebra over $\mathbb{C}$. For an element $w$ in the Weyl group $W$ …

Work in the context of a finite dimensional simple Lie algebra over $\mathbb{C}$. Write $W$ for the Weyl group and $\leq$ for the Bruhat order. For $w\in W$ let $\Delta_w$ denote t …

In Chriss and Ginzburg's book "Representation Theory and Complex Geometry" as well as the paper "Geometric Methods in Representation Theory of Hecke Algebras and Quantum Groups", t …

The Springer fiber, recall, is defined (briefly) with reference to a chosen unipotent matrix $U \in \mathrm{GL}_n$, and consists of all flags $0 = F_0 \subset F_1 \subset \dots \su …

Let $\mathcal{B}$ be the flag variety and $\mathcal{N} \subset \mathfrak{g}$ is the nilpotent cone. We know that the Springer resolution $$ \mu: T^*\mathcal{B}\rightarrow \mathcal{ …

Let's consider the Springer resolution of the nilpotent cone $\mathcal{N}$ of a complex semisimple Lie algebra $\mathfrak{g}$, which is $$ \widetilde{\mathcal{N}}=T^*\mathcal{B}\r …

Background Let $S_{g,n}$ be an oriented surface of genus $g$, with $n$ punctures. We explicitly prohibit the non-hyperbolic cases: $g=0$, $n=0,1,2$. $g=1$, $n=0$. Let $\Gamma …

Does there exist (as elementary as possible) a generalized flag manifold (e.g. sphere, projective space, Grassmanian, etc.) of a simple classical Lie group (SL, SO or Sp over real …

Recently I was watching a talk: http://media.cit.utexas.edu/math-grasp/Ben_Webster.html and at the end the lecturer gave a correspondence (I was having trouble with subscripts so c …

If we have a finite dimensional Lie algebra g, then the flag variety of g is a projective scheme. My question is what is Hirzebruch-Riemann-Roch formula for this projective scheme …

From the answers in noncommutative algebraic geometry, one can take abelian category as a scheme(commutative or noncommutative). So I wonder whether anyone ever developed the Groth …

Recall that a topological space is called $A$-affine for a sheaf of algebras $A$ if taking global sections of coherent sheaves of $A$-modules is an equivalence of categories to fin …

There's a well-known series of articles by Lusztig about Character Sheaves. They have important connections to many things in (geometric) representation theory, e.g. 0904.1247 How …