Place: TAU  Schreiber Mathematical Institute, room 309

Time: Tuesday,  12:10

Organizer: Evgeny Feigin  

Upcoming talks:

03.11 and 10.11.   Speaker: Arkady Berenstein (University of Oregon)

Title: Generalized electrical Lie algebras and invariants 

Abstract:  My talk is based on joint work with Azat Gainutdinov and Vassily Gorbounov, in which we generalize in several ways the electrical Lie algebras originally introduced by Lam and Pylyavskyy. To each semisimple (or Kac-Moody Lie algebra) g we associate a family of flat deformations of its nilpotent part parametrized by the points of the Cartan subalgebra of g. If g=sl_n, then the generic electrical Lie algebra is sp_{n-1}, which is simple if n is odd. Similar situation is with other classical lie algebras, for instance if g=sp_{2n}, then its generic electrical Lie algebra is sp_n \oplus sp_{n-1}, which is never semisimple.

In many cases, including classical and affine cases, the electrical Lie algebras admit ``edge models," where the deformation parameters can be viewed as edge weights of the Dynkin diagram of g. 

It turns out (yet conjecturally) that any integrable simple g-module V contains a unique, up to a scalar multiple, electrical invariant, viewed as a deformed highest weight vector. As a consequence, this gives a canonical vector in each weight subspace of V. The conjecture has been proved so far for all classical g.   

If time permits, I will introduce magnetic and even more general electromagnetic Lie algebras and explain the situation with their invariants.

17.11. Mark Shusterman (WIS)

24.11. Erez Lapid (WIS)