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GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  03 September 2021

TOSHIAKI SHOJI Open the ORCID record for TOSHIAKI SHOJI [Opens in a new window]
TOSHIAKI SHOJI*
Affiliation:
School of Mathematical Sciences Tongji University Shanghai 200092 P.R. China [email protected]
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Abstract

Lusztig’s algorithm of computing generalized Green functions of reductive groups involves an ambiguity on certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars explicitly, and eliminate the ambiguity. Our results imply that all the generalized Green functions of classical type are computable.

MSC classification

Primary: 20G40: Linear algebraic groups over finite fields
Secondary: 20G05: Representation theory
Type
Article
Information
Nagoya Mathematical Journal , Volume 247 , September 2022 , pp. 552 - 573
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Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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References

Beynon, W. M. and Spaltenstein, N., Green functions of finite Chevalley groups of type En(n = 6,7,8) , J. Algebra 88 (1984), 584–614.CrossRefGoogle Scholar
Grove, L. C., Classical Groups and Geometric Algebra, Grad. Stud. Math. 39, Amer. Math. Soc., Providence, RI, 2002.Google Scholar
Lusztig, G., Intersection cohomology complexes on a reductive group , Invent. Math. 75 (1984), 205–272.CrossRefGoogle Scholar
Lusztig, G., Character sheaves, I , Adv. Math. 56 (1985), 193–237; II, Adv. Math. 57 (1985), 226–265; III, Adv. Math. 57 (1985), 266–315; IV, Adv. Math. 59 (1986), 1–63; V, Adv. Math. 61 (1986), 103–155.CrossRefGoogle Scholar
Lusztig, G. and Spaltenstein, N., “On the generalized springer correspondence for classical groups”, in Algebraic Groups and Related Topics (ed. Hotta, R.), Adv. Studies in Pure Math. 6, North-Holland, Amsterdam, 1985, 289–316.CrossRefGoogle Scholar
Shoji, T., On the Green polynomials of Chevalley groups of type F 4 , Comm. Algebra 10 (1982), 505–543.CrossRefGoogle Scholar
Shoji, T., On the Green polynomials of classical groups , Invent. Math. 74 (1983), 237–267.CrossRefGoogle Scholar
Shoji, T., Generalized Green functions and unipotent classes for finite reductive groups, I , Nagoya Math. J. 184 (2006), 155–198; II, Nagoya Math. J. 188 (2007), 133–170.Google Scholar