Questions tagged [geometric-representation-theory]
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208 questions
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Can the Quantum Torus be realized as a Hall Algebra?
Background
The Quantum Torus
Let $q$ be an arbitrary complex number, and define (the algebra of) the quantum torus to be
$$T_q:=\mathbb{C}\langle x^{\pm 1},y^{\pm 1}\rangle/xy-qyx$$
For $q=1$, this is ...
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Weil's theorem about maps from a discrete group to a Lie group.
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 space of all the maps ...
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Is there Grothendieck Riemann Roch for abelian category?
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 Grothendieck Riemann Roch ...
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What is the Hirzebruch-Riemann-Roch formula for the flag variety of a Lie algebra?
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? Are there any ...
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6
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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 ...
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Explanation for Satake correspondence
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{disk}^\times} \...
- 15.1k
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Beilinson-Bernstein and Koszul duality
For geometric representation theorists down here.
Consider the Beilinson-Bernstein theorem:
Functor of global sections establishes
the correspondence between twisted
D-modules with fixed ...
- 15.1k
14
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How to understand character sheaves
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 to understand these ...
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