Abstract:

We use the fusion construction in twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a by-product we uniformly realize all non-spin fundamental modules for quantized enveloping algebras of classical types, and show that they admit natural crystal bases as modules for the (derived) twisted quantum affine algebra. These crystal bases are parametrized in terms of the q-wedge products. Copyright 2000 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695-8205 2: Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan