Glasnik Matematicki, Vol. 34, No.1 (1999), 73-86.
SOME CRYSTAL ROGERS-RAMANUJAN TYPE IDENTITIES
University of Zagreb, Department of Mathematics, Bijenička 30,
10000 Zagreb, Croatia
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.
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