engleski

Combinatorial bases of basic modules for affine Lie algebras C_{n}^{(1)}

J. Lepowsky and R.L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e. integrable highest weight) representations of affine Kac-Moody Lie algebras. A.~Meurman and M.~Primc developed further this approach for $\mathfrak{sl}(2,\mathbb C)\widetilde{}$ by using vertex operator algebras and Verma modules. In this paper we use the same method to construct combinatorial bases of basic modules for affine Lie algebras of type $C_{n}^{(1)}$ and, as a consequence, we obtain a series of Rogers-Ramanujan type identities. A major new insight is a combinatorial parametrization of leading terms of defining relations for level one standard modules for affine Lie algebra of type $C_{n}^{(1)}$.

Affine Kac-Moody Lie algebras ; vertex operator algebras ; integrable highest weight representations ; combinatorial bases of basic modules ; Rogers-Ramanujan type identities

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