A note on tensor categories of Lie type E9

2004/06/30 by Eric C. Rowell
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CO #math.QA #math.RT #msc:17B10 #msc:17B67 #msc:81R10

paper · pdf · doi:10.1016/j.jalgebra.2004.08.014

published as J. of Algebra, 284 (2005) no. 1, 296-309 · Final published version

openalex publication_date 2004/09/17 · arxiv created 2005/02/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra \g(E₉). We describe an elementary algorithm for determining the decomposition of the submodule of \Vn whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann's path algorithm and conforms with the uniform combinatorial behavior recently discovered by H. Wenzl for the series E_N, N\not=9.

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