The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials

被引：64

作者：

Schiffmann, O. ^{[1
]}

Vasserot, E. ^{[2
]}

机构：

[1] Univ Paris 06, Inst Math Jussieu, F-75013 Paris, France

[2] Univ Paris 07, Inst Math Jussieu, F-75013 Paris, France

来源：

COMPOSITIO MATHEMATICA | 2011年 / 147卷 / 01期

关键词：

Hall algebras; elliptic curves; Macdonald polynomials; Eisenstein series; Cherednik algebras; QUANTUM GROUPS;

D O I：

10.1112/S0010437X10004872

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (H) double over dot(n) of type GL(n) for all n. This allows us to obtain a geometric construction of the Macdonald polynomials P(lambda)(q, t(-1)) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X.

引用

页码：188 / 234

页数：47

共 21 条

[1]

[Anonymous], 2003, Abelian varieties, theta functions and the Fourier transform

[2]

Atiyah MF., 1957, Proc. London Math. Soc., V7, P414, DOI 10.1112/plms/s3-7.1.414

[3]

Bergeron F., 1999, Methods Appl. Anal., V6, P363

[4]

BURBAN I, 2005, ARXIVANATHAG0505148

[5]

CHEREDNIK I, 2004, DOUBLE AFFINE HECKE

[6]

Ginzburg V., 1995, ARXIVALGGEOM9511007

[7] HALL ALGEBRAS, HEREDITARY ALGEBRAS AND QUANTUM GROUPS [J].

GREEN, JA .

INVENTIONES MATHEMATICAE, 1995, 120 (02) :361-377

[8] CHEVALLEY GROUPS OVER FUNCTION FIELDS AND AUTOMORPHIC FORMS [J].

HARDER, G .

ANNALS OF MATHEMATICS, 1974, 100 (02) :249-306

[9] Involutions of double affine Hecke algebras [J].

Ion, B .

COMPOSITIO MATHEMATICA, 2003, 139 (01) :67-84

[10]

IWAHORI N, 1965, PUBL MATH-PARIS, V25, P5, DOI DOI 10.1007/BF02684396

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