Communications in Mathematical Physics

, Volume 224, Issue 3, pp 705–732

Tensor Product of Crystal Bases¶forUq(??}(m,n))-Modules

  • Seok-Jin Kang
  • Jae-Hoon Kwon

DOI: 10.1007/PL00005591

Cite this article as:
Kang, SJ. & Kwon, JH. Commun. Math. Phys. (2001) 224: 705. doi:10.1007/PL00005591

Abstract:

In this paper, we give a combinatorial algorithm of decomposing the tensor product of Uq(??(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 Uq(??(m,n))-crystals. Hence the connected components are parametrized by the Littlewood–Richardson tableaux.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Seok-Jin Kang
    • 1
  • Jae-Hoon Kwon
    • 2
  1. 1.School of Mathematics, Korea Institute for Advanced Study, Seoul 130-012, South Korea.¶E-mail: sjkang@kias.re.krKR
  2. 2.Department of Mathematics, College of Natural Sciences, Seoul National University, Seoul 151-747,¶South Korea. E-mail: jhkwon@math.snu.ac.krKR

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