Glasnik Matematicki, Vol. 34, No.1 (1999), 73-86.

SOME CRYSTAL ROGERS-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.

1991 Mathematics Subject Classification.   05A19, 17B37, 17B67.

Key words and phrases.   Rogers-Ramanujan identities, colored partitions, partition ideals, perfect crystals, affine Lie algebras, basic modules.