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

Max Neunhoeffer; Olivier Brunat

doi:10.1090/S1088-4165-2012-00383-1

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

Max Neunhoeffer, Olivier Brunat

Pure Mathematics

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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.

Original language	English
Journal	Represent. Theory
Volume	16
Early online date	18 Jan 2012
DOIs	https://doi.org/10.1090/S1088-4165-2012-00383-1
Publication status	E-pub ahead of print - 18 Jan 2012

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abstract = "We denote by A the ring of Laurent polynomials in the indeterminate v andby 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-degeneratesymmetrising 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, wegive a new criterion for James{\textquoteright} conjecture.",

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N2 - We denote by A the ring of Laurent polynomials in the indeterminate v andby 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-degeneratesymmetrising 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, wegive a new criterion for James’ conjecture.

AB - We denote by A the ring of Laurent polynomials in the indeterminate v andby 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-degeneratesymmetrising 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, wegive a new criterion for James’ conjecture.

UR - http://www-groups.mcs.st-and.ac.uk/~neunhoef/Publications/pdf/klqschur_submitted.pdf

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VL - 16

JO - Represent. Theory

JF - Represent. Theory

ER -

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

Abstract

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