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Home > Vol 22, No 3 (2005)

Anna Stokke

University of Winnipeg Department of Mathematics and Statistics 515 Portage Avenue, Winnipeg Manitoba Canada R3B 2E9 515 Portage Avenue, Winnipeg Manitoba Canada R3B 2E9

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.

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