Iwahori-Hecke algebras of type A at roots of unity

1996/10/28 by Frederick M. Goodman, Goodman, Frederick M., Hans Wenzl +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9610033

openalex publication_date 1996/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we explore the use of path idempotents for the Hecke algebra of type A at roots of unity. For q a primitive ℓ-th root of unity we obain a non-unital imbedding of (a quotient of) the group algebra of S_m into (a quotient of) the Hecke algebra H_n(q) for certain m and n. From this we recover certain instances of irreducibility criteria of Dipper, James, and Mathas, and we derive estimates on the decomposition numbers for the Hecke algebra at roots of unity. The bounds are easily computed, provide a good geometric picture of the pairs of diagrams λ, μ for which the decomposition number d_{λ, μ} is non-zero, and also appers to be a useful adjunct to the exact computation of the decomposition numbers.

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