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

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- by Olivier Brunat and Max Neunhöffer
- Represent. Theory
**16**(2012), 88-107 - DOI: https://doi.org/10.1090/S1088-4165-2012-00383-1
- Published electronically: January 18, 2012
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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 $\mathcal {S}_q(n,r)$ over $A$. We will associate to every symmetrising trace form $\tau$ on $K\mathcal {S}_q(n,r)$ a subalgebra $\mathcal {J}_{\tau }$ of $K\mathcal {S}_q(n,r)$ which is isomorphic to the “asymptotic” algebra $\mathcal {J}(n,r)_A$ defined by J. Du. As a consequence, we give a new hypothesis which implies James’ conjecture.## References

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## Bibliographic Information

**Olivier Brunat**- Affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, D-44780 Bochum, Germany
- Address at time of publication: Institut de Mathèmatiques de Jussieu, UFR de Mathèmatiques, 175, rue du Chevaleret, F-75013 Paris
- Email: brunat@math.jussieu.fr
**Max Neunhöffer**- Affiliation: School of Mathematics and Statistics, Mathematical Institute, North Haugh, St Andrews, Fife KY16 9SS, Scotland, United Kingdom
- Email: neunhoef@mcs.st-and.ac.uk
- Received by editor(s): January 9, 2009
- Received by editor(s) in revised form: April 2, 2010
- Published electronically: January 18, 2012
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**16**(2012), 88-107 - MSC (2010): Primary 20C08, 20F55; Secondary 20G05
- DOI: https://doi.org/10.1090/S1088-4165-2012-00383-1
- MathSciNet review: 2869019