Lunes 03/12/2018, 14:30 hs. Aula 27
Título:
Irreducible representations and discriminants via Poisson orders
Resumen:
Many problems in representation theory concern the study of
irreducible representations of algebras with large centers (universal
enveloping algebras in prime characteristic, quantum groups at roots
of unity, PI Sklyanin algebras). The notion of Poisson orders brings
strong Poisson geometric methods to these problems. We will review
this setting, the Brown-Gordon theorem for isomorphisms across
symplectic leaves, and its applications to representation theory. From
a different perspective we will describe how related Poisson geometric
methods can be used to compute the discriminants of the noncommutative
algebras in question. The last part of the talk is on a joint work
with Bach Nguyen, Kurt Trampel, Chelsea Walton and Xingting Wang.