Representation theory seminar: Hall algebras and Cherednik algebras | |
Student No.： | 50 |
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 |
Starting Date： | 2013-9-18 |
Ending Date： | 2013-12-18 |
Abstract:
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 [5]). Etingof, Oblomkov and Rains defined some generalization of Cherednik algebras and related it to weighted projective lines and multiplicative preprojective algebras (see [6]). 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.
References：
[1] K. Bruning, I. Burban: Coherent sheaves of elliptic curves. Lecture note, see homepage of Igor Burban.
[2] 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.
[3] Igor Burban, Olivier Schiffmann, On the Hall algebra of an elliptic curve, I, arXiv:math/0505148.
[4] P. Etingof, Xiaoguang Ma, Lecture notes on Cherednik algebras, arXiv: 1001.0432.
[5] O. Schiffmann, E. Vasserot, The elliptic Hall algebra, Cherednick Hecke algebras and Macdonald polynomials, arXiv:0802.4001.