Tokyo Journal of Mathematics

Pictures and Littlewood-Richardson Crystals


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We shall describe the one-to-one correspondence between the set of pictures and the set of Littlewood-Richardson crystals.

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Tokyo J. Math., Volume 34, Number 2 (2011), 493-506.

First available in Project Euclid: 30 January 2012

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Zentralblatt MATH identifier

Primary: 05E10: Combinatorial aspects of representation theory [See also 20C30]
Secondary: 17B20: Simple, semisimple, reductive (super)algebras 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]


NAKASHIMA, Toshiki; SHIMOJO, Miki. Pictures and Littlewood-Richardson Crystals. Tokyo J. Math. 34 (2011), no. 2, 493--506. doi:10.3836/tjm/1327931398.

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  • Michael Clausen and Friedrich Stötzer, Picture and Skew (Reverse) Plane Partitions, Lecture Note in Math., 969, Combinatorial Theory, 100–114.
  • Michael Clausen and Friedrich Stötzer, Pictures und Standardtableaux, Bayreuth. Math. Schr., 16 (1984), 1–122.
  • Sergey Fomin and Curtis Greene, A Littlewood-Richardson Miscellany, Europ. J. Combinatorics, 14 (1993), 191–212.
  • W. Fulton, Young tableaux, London Mathematical Society Student Text 35, Cambridge.
  • Jin. Hong and Seok-Jin Kang, Introduction to Quantum Groups and Crystal Bases, American Mathematical Society.
  • G. D. James and M. H. Peel, Specht series for skew representations of symmetric groups, J. Algebra., 56 (1979), 343–364.
  • M. Kashiwara, Crystallizing the $q$-analogue of universal enveloping algebras, Comm. Math. Phys., 133 (1990), 249–260.
  • M. Kashiwara, On crystal bases of the $q$-analogue of universal enveloping algebras, Duke Math. J., 63 (1991), 465–516.
  • T. Kitajima, “Correspondence between two Littlewood-Richardson rules”, Master Thesis of Sophia University (in, Japanese).
  • M. Kashiwara and T. Nakashima, Crystal graph for representations of the $q$-analogue of classical Lie algebras, J. Algebra., 165 (1994), 295–345.
  • T. Nakashima, Crystal Base and a Generalization of the Littlewood-Richardson Rule for the Classical Lie Algebras, Commun. Math. Phys., 154 (1993), 215–243.
  • A. V. Zelevinsky, “A generalization of the Littlewood-Richardson rule and the Robinson-Shensted-Knuth correspondence”, J. Algebra., 69 (1981), 82–94.