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 …

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, anot …

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 …

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

Suppose $G$ a reductive Lie group with finitely many connected components, and suppose in addition that the connected component $G^0$ of the identity can be expressed as a finite c …

Background The Quantum Torus Let $q$ be an arbitrary complex number, and define (the algebra of) the quantum torus to be $$T_q:=\mathbb{C}\langle x^{\pm 1},y^{\pm 1}\rangle/xy-qy …

Let K be a group (with discrete topology), G be a Lie group. Let $\operatorname{Hom}(K,G)$ be the space of all group homomorphisms from K to G. This is a closed subvariety of the s …

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 …

For geometric representation theorists down here. Consider the Beilinson-Bernstein theorem: Functor of global sections establishes the correspondence between twisted D-mo …

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 b …

Some time ago I was told there's an interesting classical Satake correspondence which I will write as $$[\mathop{\mathrm{disk}} \Rightarrow G] \,\backslash\, [\mathop{\mathrm{dis …