Iwahori-Hecke algebras of type A at roots of unity

Details Iwahori-Hecke algebras of type A at roots of unity Iwahori-Hecke algebras of type A at roots of unity

1996-10-28

arxiv.org/abs/q-alg/9610033v3

Mathematics

Quantum Algebra

**Second** substantial revision of previously submitted manuscript. 38 pages, TeX, with figures in EPS, requires macro BoxedEP

Scientific paper

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 $\lambda$, $\mu$ for which the decomposition number $d_{\lambda, \mu}$ is non-zero, and also appers to be a useful adjunct to the exact computation of the decomposition numbers.

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