## 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 iso-

morphic to the “asymptotic” algebra J (n, r)A defined by J. Du. As a consequence, we

give a new criterion for James’ conjecture.

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 iso-

morphic to the “asymptotic” algebra J (n, r)A defined by J. Du. As a consequence, we

give a new criterion for James’ conjecture.

Original language | English |
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Journal | Represent. Theory |

Volume | 16 |

Early online date | 18 Jan 2012 |

DOIs | |

Publication status | E-pub ahead of print - 18 Jan 2012 |