Actions of relative Weyl groups I, II

Details Actions of relative Weyl groups I, II Actions of relative Weyl groups I, II

2003-04-30

arxiv.org/abs/math/0304500v1

Mathematics

Group Theory

Part I is a corrected version of math.GR/0111224 (to appear in J. Group theory) : 37 pages Part II : 34 pages

Scientific paper

In the first part, we construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from the isomorphism of Lusztig by a linear character, and we relate this linear character to some stabilizers. Some consequences for characteristic functions of character sheaves are obtained. In the second part, we compute explicitly this linear character whenever the cuspidal local system is supported by the regular unipotent class and, as an application of these methods, we obtain a refinement of Digne, Lehrer and Michel's theorem on Lusztig restriction of Gel'fand-Graev characters.

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