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A further refinement of the Bruhat decomposition
Author:
Charles W. Curtis
Journal:
Proc. Amer. Math. Soc. 102 (1988), 37-42
MSC:
Primary 20G15
MathSciNet review:
915711
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Abstract: Kawanaka obtained explicit formulas for the structure constants in the Hecke algebra of a finite Chevalley group . This note contains a geometric interpretation of these formulas, involving decompositions of Bruhat cells, in connected reductive algebraic groups.
- [1]
A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55-150; ibid. 41 (1972), 253-276.
- [2]
Bomshik
Chang, Decomposition of Gelfand-Graev characters of
𝐿𝐺𝐿₃(𝑞), Comm. Algebra
4 (1976), no. 4, 375–401. MR 0401940
(53 #5766)
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Vinay
V. Deodhar, On some geometric aspects of Bruhat orderings. I. A
finer decomposition of Bruhat cells, Invent. Math. 79
(1985), no. 3, 499–511. MR 782232
(86f:20045), http://dx.doi.org/10.1007/BF01388520
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Noriaki
Kawanaka, Unipotent elements and characters of finite Chevalley
groups, Osaka J. Math. 12 (1975), no. 2,
523–554. MR 0384914
(52 #5784)
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Robert
Steinberg, Lectures on Chevalley groups, Yale University, New
Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
(57 #6215)
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Takeo
Yokonuma, Sur le commutant d’une représentation
d’un groupe de Chevalley fini, C. R. Acad. Sci. Paris
Sér. A-B 264 (1967), A433–A436 (French). MR 0212102
(35 #2977)
- [1]
- A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55-150; ibid. 41 (1972), 253-276.
- [2]
- B. Chang, Decomposition of Gelfand-Graev characters of
, Comm. Algebra 4 (1976), 375-401. MR 0401940 (53:5766)
- [3]
- V. Deodhar, On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells, Invent. Math. 79 (1985), 499-511. MR 782232 (86f:20045)
- [4]
- N. Kawanaka, Unipotent elements and characters of finite Chevalley groups, Osaka J. Math. 12 (1975), 523-554. MR 0384914 (52:5784)
- [5]
- R. Steinberg, Lectures on Chevalley groups, Yale University, 1967. MR 0466335 (57:6215)
- [6]
- T. Yokonuma, Sur le commutant d'une représentation d'un groupe de Chevalley fini, C. R. Acad. Sci. Paris 264 (1967), 433-436. MR 0212102 (35:2977)
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DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0915711-3
PII:
S 0002-9939(1988)0915711-3
Keywords:
Reductive algebraic groups,
Bruhat decomposition,
Hecke algebra
Article copyright:
© Copyright 1988 American Mathematical Society
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