Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11312
Title: Key polynomials, invariant factors and an action of the symmetric group on Young tableaux
Authors: Azenhas, Olga 
Mamede, Ricardo 
Keywords: Action of the symmetric group on Young tableaux; Frank words; Invariant factors; jeu de taquin; Key polynomials and matrices over a local principal ideal domain
Issue Date: 2006
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 06-62 (2006)
Abstract: We give a combinatorial description of the invariant factors associated with certain sequences of product of matrices, over a local principal ideal domain, under the action of the symmetric group by place permutation. Lascoux and Sch¨utzenberger have defined a permutation on a Young tableau to associate to each Knuth class a right and left key which they have used to give a combinatorial description of a key polynomial. The action of the symmetric group on the sequence of invariant factors generalizes this action of the symmetric group, by Lascoux and Sch¨utzenberger, to Young tableaux of the same shape and weight. As a dual translation, we obtain an action of the symmetric group on words congruent with key-tableaux based on nonstandard pairing of parentheses.
URI: http://hdl.handle.net/10316/11312
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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