(University of Sydney)
Friday 16th September, 12.05-12.55pm, Carslaw 275
Verma modules for Yangians
Although the representation theory of Yangians is quite developed,
some elementary questions have remained unanswered.
We answer some of them in a joint paper with Y. Billig and V. Futorny
by giving an irreducibility criterion for the Verma modules
over the Yangians. Like for representations of the
simple Lie algebras, every Verma module over a Yangian
has a unique irreducible quotient. We also give necessary
and sufficient conditions for the weight spaces of this quotient to be
finite-dimensional. In the A type, these conditions
were found independently by Brundan and Kleshchev.