Institut für Mathematik

Vortrag

Modul:   MAT591  Discrete mathematics

Rogers-Ramanujan type identities and representation theory of affine Lie algebras

Vortrag von Dr. Tomislav Sikic

Sprecher eingeladen von: Prof. Dr. Valentin Féray

Datum: 23.04.18   Zeit: 14.00 - 14.45   Raum: Y27H26

At the beginning of this talk it will be given a brief historical overview of results related to Rogers-Ramanujan type identities and representation theory of affine Lie algebras. Especially, the historic vertical based on the Lepowsky-Wilson approach (1981) will be highlighted. In the rest of the talk it will be presented the construction of combinatorial bases of basic and standard modules for affine symplectic Lie algebras \( C^{(1)}_n \).

Special accent of this talk will be devoted to the combinatorial parametrization of the leading terms of defining relations for standard modules for the affine Lie algebra of type \(C^{(1)}_n \). This parametrization is the base of a conjecture on the existence of combinatorial bases of level $k$ standard modules and the corresponding colored Rogers-Ramanujan type combinatorial identities where \( n\geq 2 \) and \( k\geq 2 \). The numerical evidence for some characteristic examples which supports our conjecture will be given. At the end of the talk, it will be discussed how these results can be interpreted as a generalization of the Capparelli identities and where is the connection with Jehanne Dousse's work.

This talk is based on joint work with Mirko Primc.