An involution based left ideal in the Hecke algebra

2015/07/08 by G. Lusztig, Lusztig, G. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1507.02263

openalex publication_date 2015/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an imbedding of the Hecke algebra module carried by the involutions in a Weyl group W (defined by the author and Vogan) into a completion of the Hecke algebra. An analogous result is proved for any Coxeter group. A variant of the construction gives an imbedding of the biregular representation of a Hecke algebra of W in a completion of the Hecke algebra of W².

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• Positivity for certain Weyl group representations

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