Tokyo Journal of Mathematics

RSK Type Correspondence of Pictures and Littlewood-Richardson Crystals

Toshiki NAKASHIMA and Miki SHIMOJO

Full-text: Open access

Abstract

We present a Robinson-Schensted-Knuth type one-to-one correspondence between the set of pictures and the set of pairs of Littlewood-Richardson crystals.

Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 113-130.

Dates
First available in Project Euclid: 22 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1374497514

Digital Object Identifier
doi:10.3836/tjm/1374497514

Mathematical Reviews number (MathSciNet)
MR3112378

Zentralblatt MATH identifier
1273.05236

Citation

NAKASHIMA, Toshiki; SHIMOJO, Miki. RSK Type Correspondence of Pictures and Littlewood-Richardson Crystals. Tokyo J. Math. 36 (2013), no. 1, 113--130. doi:10.3836/tjm/1374497514. https://projecteuclid.org/euclid.tjm/1374497514


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References

  • 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, Commun. 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.
  • M. Kashiwara and T. Nakashima, Crystal graph for representations of the $q$-analogue of classical Lie algebras, J. Algebra 165 (1994), Number 2, 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.
  • T. Nakashima and M. Shimojo, Pictures and Littlewood-Richardson Crystals, Tokyo J. Math. 34 (2011), 493–506.
  • T. Nakashima and M. Shimojo, Admissible Pictures and Littlewood-Richardson Crystals, Commum. in Algebra 39: 10 (2011), 3849–3865.
  • Marc A. A. van Leeuwen, Tableau algorithms defined naturally for pictures. Proceedings of the 6th Conference on Formal Power Series and Algebraic Combinatorics (New Brunswick, NJ, 1994). Discrete Math. 157 (1996), no. 1–3, 321–362.
  • A. V. Zelevinsky, A Generalization of the Littlewood-Richardson Rule and the Robinson-Schensted-Knuth Correspondence, J. Algebra 69 (1981), 82–94.