A Quantum Version of the Désarménien Matrix

    loading  Checking for direct PDF access through Ovid


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.

    loading  Loading Related Articles