Geodesic
A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 427-449.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A _{+\infty }$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers Sagan and Stanley's correspondence for skew tableaux as its restriction.
Keywords: keywords plactic algebra, crystal, Schur operator 
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     author = {Kwon, Jae-Hoon},
     title = {A plactic algebra of extremal weight crystals and the {Cauchy} identity for {Schur} operators},
     journal = {Journal of Algebraic Combinatorics},
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Kwon, Jae-Hoon. A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 427-449. http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a3/