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

2008/10/14 by Olivier Brunat, Brunat, Olivier, Max Neunhöffer +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0810.2335

arxiv created 2008/10/14 · openalex publication_date 2008/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S_q(n,r) over A. We will associate to every non-degenerate symmetrising trace form τon KS_q(n,r) a subalgebra J_τ of KS_q(n,r) which is isomorphic to the "asymptotic" algebra \J(n,r)_A defined by J. Du. As a consequence, we give a new criterion for James' conjecture.

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