Duality for Representations of a Reductive Group over a Finite Field, II
نویسنده
چکیده
This paper is a continuation of 161 whose notations and references we shall preserve. 6 Let 1 be a prime number, (I, q) = 1, and let 8, be an algebraic closure of 0,. Let .9(G) be the Grothendieck group of virtual G-modules over a,. for any finite-dimensional G-module E over 8,. Let T be a maximal torus of G, defined over F, and let T be the group of its F,-rational points. For any one dimensional T-module 0 (over a,) we have defined in [5, 1.201 a virtual representation R:(B). Let u(G) be the F,-rank of G. We shall prove the following: THEOREM. Let us recall the definition of R:(8) or, more generally, that of " twisted induction " from Levi subgroups (cf. [S, 71).
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Duality for Representations of a Reductive Group over a Finite Field
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