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The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials
- Part of
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- Journal:
- Compositio Mathematica / Volume 147 / Issue 1 / January 2011
- Published online by Cambridge University Press:
- 07 July 2010, pp. 188-234
- Print publication:
- January 2011
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- Article
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We exhibit a strong link between the Hall algebra HX of an elliptic curve X defined over a finite field 𝔽l (or, more precisely, its spherical subalgebra U+X) and Cherednik’s double affine Hecke algebras
of type GLn, for all n. This allows us to obtain a geometric construction of the Macdonald polynomials Pλ(q,t−1) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X.
of type GL