Colloquium of the ZMP: Anatomy of big algebras

by Dr Tamás Hausel (ISTA)

Thursday 27 Jun 2024, 16:15 → 17:45 Europe/Berlin

H2 (GEOMATIKUM)

Big algebras are maximal commutative subalgebras of Kirillov algebras attached to irreducible representations of a complex semisimple Lie group. They can be motivated by mirror symmetry for Langlands dual Hitchin systems. In this talk we will visualize the anatomy of big algebras, in terms of skeletons and nerves. We show that they encode sophisticated information of the representation, such as a ring structure on multiplicity spaces, the weight diagram and the crystal structure.