$q$-Wedge Modules for Quantized Enveloping Algebras of Classical Type

Abstract

We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct 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.

20 pages, Latex file

References in corpus (1)

• Excitation Spectra of Spin Models constructed from Quantized Affine Algebras of type $B_n^{(1)}$, $D_n^{(1)}$

Cited by in corpus (23)

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• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
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• Wedge modules for two-parameter quantum groups
• Virtual crystals and fermionic formulas of type $D_{n+1}^{(2)}$, $A_{2n}^{(2)}$, and $C_n^{(1)}$
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• Applications of Crystal Bases to Current Problems in Representation Theory
• An algorithm for computing the global basis of a finite dimensional irreducible $U_q(s{o}_{2n+1})$ or $U_q(s{o}_{2n})$-module
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• On fusion procedure for the two-parameter quantum algebra in type A
• On the structure and representation theory of $q$-deformed Clifford algebras
• Existence of Crystal Bases for Kirillov-Reshetikhin Modules of Type D
• Braided Symmetric Algebras of Simple $U_q(s{l}_2)$-Modules and Their Geometry
• Equivariant Quantizations of Symmetric Algebras
• R-Matrix Poisson Algebras and Their Deformations