On Lusztig's conjecture for connected and disconnected exceptional groups

Details On Lusztig's conjecture for connected and disconnected exceptional groups On Lusztig's conjecture for connected and disconnected exceptional groups

2006-10-16

arxiv.org/abs/math/0610476v1

Mathematics

Representation Theory

25 pages

Scientific paper

Lusztig conjectured that the almost characters of a finite reductive group are up to a scalar the same as the characteristic functions of the rational character sheaves defined on the corresponding algebraic group. We propose in this paper to verify this conjecture for the uniform almost characters of the Suzuki and the Ree groups and to show that a conjecture of the same type holds for the disconnected case of type B_2. We then state a conjecture on the possible values of the uniform almost characters on unipotent elements in the disconnected case of type F_4.

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