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Crystal bases of the Fock space representations and string functions
Cited 14 time in
Web of Science
Cited 16 time in Scopus
- Authors
- Issue Date
- 2004
- Publisher
- Elsevier
- Citation
- J. Algebra 280 (2004) 313-349
- Abstract
- Let U_q(g) be the quantum affine algebra of type A_n^(1), A_2n−1^(2), A_2n^(2), B_n^(1), D_n^(1), and D_n+1^(2), and let F(Λ) be the Fock space representation for a level 1 dominant integral weight Λ. Using the crystal basis of F(Λ) and its characterization in terms of abacus, we construct an explicit bijection between the set of weight vectors in F(Λ)_{λ-m \delta} (m \geq 0) for a maximal weight λ and the set of certain ordered sequences of partitions. As a corollary, we obtain the string function of the basic representation V(Λ).
- ISSN
- 0021-8693
- Language
- English
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