Naslov
Basic representations for classical affine Lie algebras

Autori
Primc, Mirko

Izvornik
Journal of Algebra (0021-8693) 228 (2000); 1-50

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
affine Lie algebras; vertex operator formulas; energy functions on crystals

Sažetak
Presented here is a construction of certain bases of basic representations for classical affine Lie algebras. The starting point is a Z-grading g = g_{-1} + g_0 + g_1 of a classical Lie algebra g and the corresponding decomposition tilde g = tilde g_{-1} + tilde g_0 + tilde g_1 of the affine Lie algebra tilde g. By using a generalization of Frenkel-Kac vertex operator formula for A_1^(1) one can construct a spanning set of the basic tilde g-module in terms of monomials in basis elements of tilde g_1 and certain group element e. These monomials satisfy certain combinatorial Rogers-Ramanujan type difference conditions arising from the vertex operator formula, and the main result is that these differences coincide with the energy function of a perfect crystal corresponding to the g_0-module g_1. The linear independence of the constructed spanning set of the basic tilde g-module is proved by using a crystal base character formula for standard modules due to S.-J. Kang, M. Kashiwara, K.C. Misra, T. Miwa, T. Nakashima and A. Nakayashiki.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA