8th Croatian Mathematical Congress

Combinatorial bases of standard modules for twisted affine Lie algebras

2 Jul 2024, 11:20

35m

D1 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Invited lecture ALG: Algebra Invited lectures

Speaker

Marijana Butorac

Description

We consider principal subspaces and Feigin-Stoyanovsky's type subspaces associated with integrable highest weight modules of affine Kac-Moody Lie algebras. By using the quasi-particle bases of principal subspaces, we construct combinatorial bases of the standard modules of rectangular highest weights and their parafermionic spaces for twisted affine Lie algebras. From quasi-particle bases, we obtain characters of parafermionic spaces and standard modules. We also discuss how vertex algebraic methods can be applied to the construction of combinatorial bases of Feigin-Stoyanovsky's type subspaces associated to level one standard modules of twisted affine Lie algebra of type $D_{l+1}^{(2)}$.