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Representation Theory

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Lusztig's conjecture for finite special linear groups

Author: Toshiaki Shoji
Journal: Represent. Theory 10 (2006), 164-222
MSC (2000): Primary 20G40, 20G05
Published electronically: March 22, 2006
MathSciNet review: 2219112
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Abstract: In this paper, we prove Lusztig's conjecture for $ G^F = SL_n(\mathbf F_q)$, i.e., we show that characteristic functions of character sheaves of $ G^F$ coincide with almost characters of $ G^F$ up to scalar constants, assuming that the characteristic of $ \mathbf F_q$ is not too small. We determine these scalars explicitly. Our result gives a method of computing irreducible characters of $ G^F$.

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Toshiaki Shoji
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

Received by editor(s): February 16, 2005
Received by editor(s) in revised form: January 24, 2006
Published electronically: March 22, 2006
Dedicated: To Noriaki Kawanaka on his sixtieth birthday
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.