Olga Azenhas; Ricardo Mamede;
Key polynomials, invariant factors and an action of the symmetric group on Young tableaux
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 Schutzenberger 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 Schutzenberger, 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.
Pré-publicações do Departamento de Matemática da Universidade de Coimbra