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6. Deligne-Lusztig Induction and Fourier Transforms

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1859)

Abstract

Throughout this chapter, unless specified, we assume that the prime p is acceptable for G and that q is large enough such that the geometrical induction coincides with Deligne-Lusztig induction. Fourier transforms considered will be with respect to \((\mu,\Psi)\) as in (5.2). The goal of the chapter is to discuss the commutation formula conjectured in 3.2.30. We reduce this conjecture to the case where the function f of 3.2.30 is the characteristic function of a cuspidal nilpotently supported F-equivariant orbital perverse sheaf. We then prove the conjecture in almost all cases under a stronger assumption on p.

Mathematics Subject Classification (2000):

  • 20C33

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Correspondence to Emmanuel Letellier .

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© 2005 Springer-Verlag Berlin/Heidelberg

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Letellier, E. (2005). 6. Deligne-Lusztig Induction and Fourier Transforms. In: Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras. Lecture Notes in Mathematics, vol 1859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31561-2_6

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