Original scientific paper

Some crystal Roger-Ramanujan type identities

Mirko Primc

Abstract

By using the KMN2 crystal base character formula for the basic A2(1)-module, and the principally specialized Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorial identity for colored partitions. The difference conditions between parts are given by the energy function of certain perfect A2(1)-crystal. We also recall some other identities for this type of colored partitions, but coming from the vertex operator constructions and with no apparent connection to the crystal base theory.

Keywords

Rogers-Ramanujan identities; colored partitions; partition ideals; perfect crystals; affine Lie algebras; basic modules

Hrčak ID:

6404

URI

https://hrcak.srce.hr/6404

Publication date:

1.6.1999.

Visits: 1.459 *