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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", the group algebra $\m …

Let $k$ be a field and $X$ be a topological space. We consider Sh$(X)$, the category of sheaves of $k$-vector spaces on $X$. Let $G$ be a topological group which act on $X$ continuously from the left …

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 \mathcal{N …

Let $G$ be a real semisimple Lie group and $K$ a maximal compact subgroup. Let $\mathfrak{g}$ and $\mathfrak{k}$ be the complexified Lie algebra of $G$ and $K$, respectively. Then the Hecke algebra …

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

Let $G$ be a real semisimple Lie group, $K$ be a maximal compact subgroup. Let $\mathfrak{g}_0$ and $\mathfrak{k}_0$ be their real Lie algebras respectively. Let $\mathfrak{g}$ and $\mathfrak{k}$ be t …