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Lectures on Quantum Groups
Revised second edition. The text covers the material presented for a graduate-level course on quantum groups at Harvard University. Covered topics include: Poisson algebras and quantization,
Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2
We construct a representation of the affine W-algebra of ${\mathfrak{g}}{\mathfrak{l}}_{r}$ on the equivariant homology space of the moduli space of Ur-instantons, and we identify the corresponding
On the Hall algebra of an elliptic curve, I
This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to
Quantum Groups and Lie Theory: Lectures on the dynamical Yang-Baxter Equations
This paper contains a systematic and elementary introduction to a new area of the theory of quantum groups -- the theory of the classical and quantum dynamical Yang-Baxter equations. It arose from a
The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of $\mathbb{A}^2$
In this paper we compute the convolution algebra in the equivariant K-theory of the Hilbert scheme of A^2. We show that it is isomorphic to the elliptic Hall algebra, and hence to the spherical DAHA
Explicit quantization of dynamical r-matrices for finite dimensional semisimple Lie algebras
1.1. Classical r-matrices. In the early eighties, Belavin and Drinfeld [BD] classified nonskewsymmetric classical r-matrices for simple Lie algebras. It turned out that such r-matrices, up to
Lectures on Hall algebras
These notes represent the written, expanded and improved version of a series of lectures given at the winter school “Representation theory and related topics” held at the ICTP in Trieste in January
Indecomposable vector bundles and stable Higgs bundles over smooth projective curves
We prove that the number of geometrically indecomposable vector bundles of xed rank r and degree d over a smooth projective curve X dened over a nite eld is given by a polynomial (depending only on
Hall algebras of curves, commuting varieties and Langlands duality
We construct an isomorphism between the (universal) spherical Hall algebra of a smooth projective curve of genus g and a convolution algebra in the (equivariant) K-theory of the genus g commuting