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Tensor Product of Crystal Bases for U_q(gl(m, n))-Modules

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Authors
Kang, Seok-Jin; Kwon, Jae-Hoon
Issue Date
2001
Publisher
Springer Verlag
Citation
Comm. Math. Phys. 224, 705-732
Keywords
U_q (gl(m, n))-crystal(m, n)-hook semistandard tableauxLittlewood–Richardson tableauxgenuine highest weight vector
Abstract
In this paper, we give a combinatorial algorithm of decomposing the tensor
product of U_q(gl(m, n))-crystals. Using the insertion scheme for (m, n)-hook semistandard
tableaux, we show that there exists a bijection between the set of Littlewood–
Richardson tableaux and the set of genuine highest weight vectors in the tensor product
of U_q(gl(m, n))-crystals. Hence the connected components are parametrized by the
Littlewood–Richardson tableaux.
ISSN
0010-3616 (Print)
1432-0916 (Online)
Language
English
URI
http://hdl.handle.net/10371/11866
DOI
https://doi.org/10.1007/PL00005591
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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