Year: 2010
Type: article
Abstract: We exhibit a strong link between the Hall algebra H X of an elliptic curve X defined over a finite field 𝔽 l (or, more precisely, its spherical subalgebra U + X ) and Cherednik’s double affine Hecke algebras $\ddot {\mathbf {H}}_n$ of type GL n , for all n . This allows us to obtain a geometric construction of the Macdonald polynomials P λ ( q , t −1 ) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X .
Source: Compositio Mathematica
Authors: O. Schiffmann, E. Vasserot
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2024918451