Meinolf Geck

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CHEVIE is a computer algebra package which collects data and programs for the representation theory of finite groups of Lie type and associated structures. We explain the theoretical and conceptual background of the various parts of CHEVIE and we show the usage of the system by means of explicit examples. More precisely, we have sections on Weyl groups and(More)
The work of Dipper and James on Iwahori-Hecke algebras associated with the finite Weyl groups of type An has shown that these algebras behave in many ways like group algebras of finite groups. Moreover, there are “generic” features in the modular representation theory of these algebras which, at present, can only be verified in examples by explicit(More)
We apply Lusztig’s theory of cells and asymptotic algebras to the Iwahori–Hecke algebra of a finite Weyl group extended by a group of graph automorphisms. This yields general results about splitting fields (extending earlier results by Digne–Michel) and decomposition matrices (generalizing earlier results by the author). Our main application is to establish(More)
We consider a generic Iwahori–Hecke algebra HO associated with a finite Weyl group, defined over a suitable discrete valuation ring O. We define filtrations on HO-modules in terms of Lusztig’s afunction. For a projective module, we show that the quotients of this filtration are direct sums of irreducible lattices. As an application, we prove refinements of(More)
Let H be the one-parameter Hecke algebra associated to a finite Weyl group W , defined over a ground ring in which “bad” primes for W are invertible. Using the Kazhdan–Lusztig basis of H, we show that H has a natural cellular structure in the sense of Graham and Lehrer. Previously, this was only known in type An and Bn. Thus, we obtain a general theory of(More)
In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative” setting, with respect to a parabolic subgroup WI ⊆ W . This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multi-parameter) Iwahori–Hecke algebra with respect to WI . We obtain two applications to the “asymptotic case” in type Bn, as(More)
We present a formalization using data uniquely de ned at the level of the Weyl group of the construction and combinatorial properties of unipotent character shea ves and unipotent characters for reductive algebraic groups over an algebraic closure of a nite eld This formalization extends to the case where the Weyl group is re placed by a complex re ection(More)
The necessity for two types of thioredoxins (Trx f and m) within chloroplasts of higher plants that mediate the same redox chemistry with various target enzymes is not well understood. To approach this complex issue, we have applied site-directed mutagenesis to the identification of residues of Trx f that affect its binding to and selectivity for target(More)
Hecke algebras arise naturally in the representation theory of nite or p-adic Cheval-ley groups, as endomorphism algebras of certain induced representations (see Carter 9], Lusztig 42], and the references there). They may also be viewed as quotients of group algebras of Artin{Tits braid groups, and then they can be used to construct invariants of knots and(More)