Iwahori-Hecke algebras of type A at roots of unity

Frederick M. Goodman; Hans Wenzl

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arXiv · q-alg/9610033

Iwahori-Hecke algebras of type A at roots of unity

Frederick M. Goodman·Hans Wenzl

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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 $\ell$-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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BibTeX RIS

Frederick M. Goodman, Hans Wenzl. 1998-10-30. Iwahori-Hecke algebras of type A at roots of unity. https://arxiv.org/abs/q-alg/9610033

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