engleski

Quasi-particles in the principal picture of sl^2 and Rogers–Ramanujan-type identities

In their seminal work Lepowsky and Wilson gave a vertex-operator theoretic interpretation of Gordon–Andrews–Bressoud’s generalization of Rogers-Ramanujan combinatorial identities, by constructing bases of vacuum spaces for the principal Heisenberg subalgebra of standard slˆ2-modules, parametrized with partitions satisfying certain difference 2 conditions. In this paper, we define quasi-particles in the principal picture of slˆ2 and construct quasi-particle monomial bases of standard slˆ2-modules for which principally specialized characters are given as products of sum sides of the corresponding analytic Rogers–Ramanujan-type identities with the character of the Fock space for the principal Heisenberg subalgebra.

Rogers-Ramanujan identities ; affine Lie algebras ; quasi-particles

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