Emmy-Noether-Seminar: Rogers-Ramanujan exact sequences and free modules over free generalized vertex algebras

Rogers-Ramanujan exact sequences and free modules over free generalized vertex algebras

Kazuya Kawasetsu (Kumamoto)

Abstract: In this talk, we introduce the notion of free modules over (generalized) vertex algebras. A series of recursion formulas, which generalizes a classical formula used to prove the famous Rogers-Ramanujan (RR) identities and RR continued fraction formula, is conceptually obtained from short exact sequences among free modules over free generalized vertex algebras, the RR exact sequences. They include as a special case one equivalent to the exact sequence constructed by S. Capparelli et al. using intertwining operators in the theory of vertex operator algebras. Applications of the RR exact sequences to combinatorics and related areas are given.