Generic character sheaves on groups over k[∊]/[∊]r

Abstract

Let k be an algebraic closure of the finite field F[subscript q] with q elements where q is a power of a prime number p. Let G be a connected reductive group over k with a fixed split F[subscript q]-rational structure, a fixed Borel subgroup B defined over F[subscript q], with unipotent radical U and a fixed maximal torus T of B defined over F[subscript q]. Let g, b, t, n be the Lie algebras of G, B, T, U. We fix a prime number l ≠ p. If λ : T(F[subscript q]) → [line over Q][subscript * under superscript l] is a character, we can lift λ to a character λ˜ : B(F[subscript q]) → [line over Q][subscript * under superscript l] trivial on U(F[subscript q]) and we can form the induced representation [mathematical figure; see resource] of G(F[subscript q]). [First paragraph] ©2017