\(q\)-wedge modules for quantized enveloping algebras of classical type. (English) Zbl 1024.17012
The authors 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 they 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 qunantum affine algebra. These crystal bases are parametrized in terms of the \(q\)-wedge products.
Reviewer: Li Fang (Hangzhou)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
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