Vertex algebras and combinatorial identities (Q1862250)

The author describes a line of research that ties together various branches of mathematics: the representation theory of affine Kac-Moody Lie algebras, vertex operator algebras, quantum groups and crystal bases, statistical mechanics, and combinatorial identities of the Rogers-Ramanujan type. He then describes in some detail some of his and A. Meurman's recent work on annihilating fields, as well as Feigin and Stoyanovsky's principal subspace ideas. Finally the author argues that one possible way to deal with the proof of linear independence of the proposed spanning sets could be through the crystal base theory for quantum groups.