2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171453We 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 τon KS_q(n,r) a subalgebra J_τ 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.Representation Theorytext