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Fix a nonarchimedean local field $L/\mathbb{Q}_p$ with ring of integers $\mathcal{O}$, uniformizer $\varpi$, and residue field $k$. If I take a matrix $$\begin{pmatrix} a & \varpi b \\ c & d \...

Let $G$ be a connected, compact Lie group, $T$ a maximal torus. Let $LG$ be the group of smooth (or polynomial) loops and $X=LG/T$ the affine flag variety ($T$ acts say by right multiplication). In ...

Let $G$ be a split reductive group over local field $F$, $G^L$ be the (complex) Langlands dual group of $G$. Denote $H$ to be the $\mathbb{Z}$-Hecke algebra of $G$, that is the ring of $G(\mathcal{O}...

Let $G=GL_n$. Let us start with the Hecke algebra $H_n$. It acts on K(constructible sheaves on $G/B$) by Hecke correpondences and on K(coherent sheaves on $G/B$) by Lusztig's construction [1]. Now we ...