A new construction of the asymptotic algebra associated to the q-Schur algebra
Abstract
We denote by A the ring of Laurent polynomials in the indeterminate v and by K its field of fractions. In this paper, we are interested in representation theory of the "generic" q-Schur algebra Sq(n,r) over A. We will associate to every non-degenerate symmetrising trace form τ on KSq(n,r) a subalgebra Jτ of KSq(n,r) which is isomorphic to the "asymptotic" algebra (n,r)A defined by J. Du. As a consequence, we give a new criterion for James' conjecture.
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