Leading terms of relations for standard modules of the affine Lie algebras $$C_{n}^{(1)}$$ C n ( 1 )

Abstract

In this paper, we give a combinatorial parametrization of leading terms of defining relations for the vacuum level k standard modules for the affine Lie algebra of type $$C_{n}^{(1)}$$ . Using this parametrization, we conjecture colored Rogers–Ramanujan type combinatorial identities for $$n\ge 2$$ and $$k\ge 2$$ ; the identity in the case $$n=k=1$$ is equivalent to one of Capparelli’s identities.