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Crystal bases of the Fock space representations and string functions

Cited 12 time in Web of Science Cited 14 time in Scopus
Authors
Kang, Seok-Jin; Kwon, Jae-Hoon
Issue Date
2004
Publisher
Elsevier
Citation
J. Algebra 280 (2004) 313-349
Keywords
Quantum affine algebraFock space representationCrystal basisString function
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
URI
http://hdl.handle.net/10371/12156
DOI
https://doi.org/10.1016/j.jalgebra.2004.04.013
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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