A new construction of the asymptotic algebra associated to the $q$-Schur algebra

Details A new construction of the asymptotic algebra associated to the $q$-Schur algebra A new construction of the asymptotic algebra associated to the $q$-Schur algebra

2008-10-14

arxiv.org/abs/0810.2335v1

Mathematics

Representation Theory

Scientific paper

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 S_q(n,r) over A. We will associate to every non-degenerate symmetrising trace form \tau on KS_q(n,r) a subalgebra J_{\tau} of KS_q(n,r) which is isomorphic to the "asymptotic" algebra \J(n,r)_A defined by J. Du. As a consequence, we give a new criterion for James' conjecture.

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