Monodromy and cactus group actions on crystals
Event details
| Date | 16.06.2015 |
| Hour | 14:15 › 15:00 |
| Speaker | Iva Halacheva, Toronto |
| Location | |
| Category | Conferences - Seminars |
In earlier work, Henriques and Kamnitzer define a cactus group action on tensor products of crystals of any finite-dimensional complex reductive Lie algebra g. We generalize the notion of a cactus group and define its action on a single crystal via Schutzenberger involutions. On the other hand, Mishchenko and Fomenko construct a family of maximal commutative subalgebras of U(g). In type A, given any representation we show there is a monodromy action coming from a cover of the moduli space parametrizing the family of subalgebras, which agrees with the cactus group action. We conjecture that this is also true in general.
Practical information
- Informed public
- Free
Organizer
- Joel Kamnitzer, Prof. Invité, Toronto