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

Authors: Olivier Brunat and Max Neunhöffer
Journal: Represent. Theory 16 (2012), 88-107
MSC (2010): Primary 20C08, 20F55; Secondary 20G05
Posted: January 18, 2012
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Abstract: We denote by the ring of Laurent polynomials in the indeterminate and by its field of fractions. In this paper, we are interested in representation theory of the ``generic'' -Schur algebra $\mathcal {S}_q(n,r)$ over . 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.

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