|Representation theory seminar: Hall algebras and Cherednik algebras|
|Time：||15:10-17:00 (Wed.), 09-18~12-18|
|Instructor：||Bangming Deng,Xiaoguang Ma,Fan Xu|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
Recently, Schiffmann and Vasserot showed that there exists a strong relation between Hall algebras of elliptic curves and double affine Hecke algebras (also called Cherednik algebras) of GL(n) (see ). Etingof, Oblomkov and Rains defined some generalization of Cherednik algebras and related it to weighted projective lines and multiplicative preprojective algebras (see ). The aim of this seminar is to understand these results.
(1) Categories of coherent sheaves of weighted projective lines;
(2) Categories of coherent sheaves of elliptic curves;
(3) Hall algebras of weighted projective lines and elliptic curves;
(4) Double affine Hecke algebras;
If time permits,
(5) The theorem of Etingof, Oblomkov and Rains;
(6) The relation between Hall algebras of elliptic curves and Cherednik algebras.
 K. Bruning, I. Burban: Coherent sheaves of elliptic curves. Lecture note, see homepage of Igor Burban.
 W. Geigle and H. Lenzing, A class of weighted projective curves arising in representation theory of ﬁnite-dimensional algebras, in Singularities, representation of algebras, and vector bundles (Lambrecht, 1985), 265–297, Lecture Notes in Math., 1273, Springer, Berlin, 1987.
 Igor Burban, Olivier Schiffmann, On the Hall algebra of an elliptic curve, I, arXiv:math/0505148.
 P. Etingof, Xiaoguang Ma, Lecture notes on Cherednik algebras, arXiv: 1001.0432.
 O. Schiffmann, E. Vasserot, The elliptic Hall algebra, Cherednick Hecke algebras and Macdonald polynomials, arXiv:0802.4001.