The decomposition numbers of the Hecke algebra of type

Author:
Meinolf Geck

Journal:
Math. Comp. **61** (1993), 889-899

MSC:
Primary 20C20

DOI:
https://doi.org/10.1090/S0025-5718-1993-1195429-5

MathSciNet review:
1195429

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Abstract: Let be the Chevalley group of type , over a finite field with *q* elements, *l* be a prime not dividing *q*, and be the endomorphism ring of the permutation representation (over a valuation ring *R* with residue class field of characteristic *l*) of on the cosets of a standard Borel subgroup . Then the *l*-modular decomposition matrix of the algebra is a submatrix of the *l*-modular decomposition matrix of the finite group . In this paper we determine the matrices , for all *l, q* as above. For this purpose, we consider the generic Hecke algebra *H* associated with the finite Weyl group of type over the ring of Laurent polynomials in an indeterminate *v*, and calculate the decomposition matrices of *H* which are associated with specializations of *v* to roots of unity over or values in a finite field. The computations were done by using the computer algebra systems MAPLE and GAP.

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1195429-5

Article copyright:
© Copyright 1993
American Mathematical Society