Quasiparticles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and RogersRamanujantype identities
Abstract
In their seminal work J. Lepowsky and R. L. Wilson gave a vertexoperator theoretic interpretation of GordonAndrewsBressoud's generalization of RogersRamanujan combinatorial identities, by constructing bases of vacuum spaces for the principal Heisenberg subalgebra of standard $\widehat{\mathfrak{sl}}_{2}$modules, parametrized with partitions satisfying certain difference 2 conditions. In this paper we define quasiparticles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and construct quasiparticle monomial bases of standard $\widehat{\mathfrak{sl}}_{2}$modules for which principally specialized characters are given as products of sum sides of the corresponding analytic RogersRamanujantype identities with the character of the Fock space for the principal Heisenberg subalgebra.
 Publication:

arXiv eprints
 Pub Date:
 June 2014
 arXiv:
 arXiv:1406.1924
 Bibcode:
 2014arXiv1406.1924K
 Keywords:

 Mathematics  Quantum Algebra;
 17B67;
 17B69 (Primary);
 05A19 (Secondary)
 EPrint:
 31 pages