Compactified Jacobians and DAHA representations
Event details
| Date | 20.09.2012 |
| Hour | 15:15 › 17:00 |
| Speaker | Eugene Gorsky, SUNY Stony Brook |
| Location | |
| Category | Conferences - Seminars |
I will describe two conjecturally equivalent descriptions of the homology
of the compactified Jacobian of a rational curve with a unique singularity
of type x^m=y^n. First, one can present an explicit cell decomposition
and match the dimensions of the cells to certain combinatorial statistics
of M. Haiman, J. Haglund and N. Loehr. In the second approach the homology
is compared to the unique finite-dimensional representation of the
rational Cherednik algebra with parameter m/n. For m=n+1, both approaches
produce a certain bivariate deformation of Catalan numbers introduced by
A. Garsia and M. Haiman.
of the compactified Jacobian of a rational curve with a unique singularity
of type x^m=y^n. First, one can present an explicit cell decomposition
and match the dimensions of the cells to certain combinatorial statistics
of M. Haiman, J. Haglund and N. Loehr. In the second approach the homology
is compared to the unique finite-dimensional representation of the
rational Cherednik algebra with parameter m/n. For m=n+1, both approaches
produce a certain bivariate deformation of Catalan numbers introduced by
A. Garsia and M. Haiman.
Practical information
- General public
- Free
Organizer
- Tamás Hausel, Chair of Geometry
Contact
- Pierrette Paulou-Vaucher, Assistant Chair of Geometry