On some representations of twisted affine Lie algebras and combinatorial identities
The aim of this paper is to give explicit vertex operator realizations of level two and level three integrable highest weight representations of the affine Lie algebra \(A_ 2^{(2)}\). Using the vertex operator realization of the basic (level one) representation of \(A_ 2^{(2)}\) and the calculus of formal variables the author obtains certain spanning sets for each level two and three representations. Invoking the Rogers- Ramanujan identities it has been shown that the spanning sets for the level two representations are in fact bases for the respective representations. It is conjectured that the spanning sets for the level three representations are also bases.
integrable highest weight representations
scientific article; zbMATH DE number 168585