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Some crystal Rogers-Ramanujan type identities

Mirko Primc
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Abstract

By using the Kang-Kashiwara-Misra-Miwa-Nakashima-Nakayashiki crystal base character formula for the basic $A_2^{(1)}$-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 $A_2^{(1)}$-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.

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BibTeXRIS

Mirko Primc. 1998-05-20. Some crystal Rogers-Ramanujan type identities. https://arxiv.org/abs/math/9805090

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