engleski

Leading terms of relations for standard modules of affine Lie algebras C_n^(1)

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 ≥ 2 and k ≥ 2 ; the identity in the case n = k = 1 is equivalent to one of Capparelli’s identities.

Affine (Kac–Moody)Lie algebras ; Vertex operator algebras ; Integrable highest weight representations ; Combinatorial bases of standard modules ; Leading terms of defining relations ; Rogers–Ramanujan type identities

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