Seminar: "Combinatorial Bases of Basic Modules for C_n^(1) and the Conjecture for All Standard Modules

Abstract: In a joint work, A. Meurman and M. Primc constructed a combinatorial
bases of integrable highest weight modules for ane Lie algebra A(1)1 . In this
construction they used vertex operator algebra theory and combinatorial argu-
ments. A "representation theory part" of that construction has been extended
to all ane Lie algebras, whereas the "combinatorial part" remained to be an
open problem for general ane Lie algebras. The similar generalized method for
construction combinatorial bases of basic modules for ane Lie algebras of type C(1)
n will be presented in this talk. Special accent of this talk will be devoted to
the combinatorial parametrization of leading terms of dening relations for all
standard modules for ane Lie algebra of type C(1)n . This parametrization is
the base of conjecture on the standard modules and the corresponding colored
Rogers-Ramanujan type combinatorial identities where n 2 and k 2; the
identity in the case n = k = 1 is equivalent to one of Capparelli's identities.

Host: John Shareshian