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7
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0answers
247 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 ...
6
votes
0answers
495 views

Is the Springer resolution a blow-up?

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}\rightarrow ...
6
votes
0answers
498 views

Hirzebruch-Riemann-Roch for quiver varieties?

These days, I attended a workshop at North Carolina State University. The key lecturer is Professor Nakajima. He introduced two types of quiver variety. One of them is affine, another one is ...
5
votes
0answers
228 views

A question about equivariant derived categories and [BBD]

Let $G$ be an algebraic group (over $\mathbb{C}$) acting algebraically on a variety $X$. Bernstein and Lunts then define in [BL94] the equivariant derived category $D^b_G(X,\mathbb{C})$ (of ...
5
votes
0answers
193 views

Action of $F_4$ on generalized flag manifolds

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 or complex field), ...
4
votes
0answers
349 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 ...
1
vote
0answers
109 views

References for crystal bases and Demazure modules in representation theory

I was wondering what are some standard general references/books/survey articles about: (1) crystal bases, and string parameterizations and (2) Demazure modules, and Schubert varieties (containing ...
0
votes
0answers
120 views

Equivariant J-function of Laumon space

Let $G=SL(n)$ and $B$ be the Borel subgroup of $G$. $G/B$ is the complete flags variety $0\subset V_1 \subset \cdots \subset V_n=\mathbb{C}^n$. The Laumon space is the space ...