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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title = "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 iso- morphic to the “asymptotic” algebra J (n, r)A defined by J. Du. As a consequence, we give a new criterion for James{\textquoteright} conjecture. ",

author = "Max Neunhoeffer and Olivier Brunat",

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T1 - A new construction of the asymptotic algebra associated to the $q$-Schur algebra

AU - Neunhoeffer, Max

AU - Brunat, Olivier

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N2 - 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.

AB - 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.

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

UR - https://www.scopus.com/pages/publications/84880696447

U2 - 10.1090/S1088-4165-2012-00383-1

DO - 10.1090/S1088-4165-2012-00383-1

M3 - Article

SN - 1088-4165

VL - 16

JO - Represent. Theory

JF - Represent. Theory

ER -

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

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