A further refinement of the Bruhat decomposition
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- by Charles W. Curtis PDF
- Proc. Amer. Math. Soc. 102 (1988), 37-42 Request permission
Abstract:
Kawanaka obtained explicit formulas for the structure constants in the Hecke algebra $H\left ( {G\left ( q \right ),B\left ( q \right )} \right )$ of a finite Chevalley group $G\left ( q \right )$. This note contains a geometric interpretation of these formulas, involving decompositions of Bruhat cells, in connected reductive algebraic groups.References
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A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55-150; ibid. 41 (1972), 253-276.
- Bomshik Chang, Decomposition of Gelfand-Graev characters of $\textrm {LGL}_{3}(q)$, Comm. Algebra 4 (1976), no. 4, 375–401. MR 401940, DOI 10.1080/00927877608822112
- 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, DOI 10.1007/BF01388520
- Noriaki Kawanaka, Unipotent elements and characters of finite Chevalley groups, Osaka Math. J. 12 (1975), no. 2, 523–554. MR 384914
- Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
- 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 212102
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 37-42
- MSC: Primary 20G15
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915711-3
- MathSciNet review: 915711