## Lusztig’s conjecture for finite special linear groups

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- by Toshiaki Shoji
- Represent. Theory
**10**(2006), 164-222 - DOI: https://doi.org/10.1090/S1088-4165-06-00275-5
- Published electronically: March 22, 2006
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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 $G^F$.## References

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## Bibliographic Information

**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
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**10**(2006), 164-222 - MSC (2000): Primary 20G40, 20G05
- DOI: https://doi.org/10.1090/S1088-4165-06-00275-5
- MathSciNet review: 2219112

Dedicated: To Noriaki Kawanaka on his sixtieth birthday