A quantum version of the Désarménien matrix.
Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 303-316.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We use elements in the quantum hyperalgebra to define a quantum version of the Désarménien matrix. We prove that our matrix is upper triangular with ones on the diagonal and that, as in the classical case, it gives a quantum straightening algorithm for quantum bideterminants. We use our matrix to give a new proof of the standard basis theorem for the $q$-Weyl module. As well, we show that the standard basis for the $q$-Weyl module and the basis dual to the standard basis for the $q$-Schur module are related by the quantum Désarménien matrix.
Mots-clés : keywords $q$-Weyl module, $q$-Schur module, désarménien matrix, quantum straightening algorithm, standard basis theorem 
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     title = {A quantum version of the {D\'esarm\'enien} matrix.},
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Stokke, Anna. A quantum version of the Désarménien matrix.. Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 303-316. https://geodesic-test.mathdoc.fr/item/JAC_2005__22_3_a3/