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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new proof of a theorem of Solomon-Tits
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by C. W. Curtis and G. I. Lehrer PDF
Proc. Amer. Math. Soc. 85 (1982), 154-156 Request permission

Abstract:

Let $\Delta$ be the combinatorial building of a finite group of Lie type $G$. A new proof is given of the theorem of Solomon-Tits on the $G$-module structure of the rational homology ${H_* }(\Delta )$ of $\Delta$.
References
  • N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
  • Charles W. Curtis, Homology representations of finite groups, Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979) Lecture Notes in Math., vol. 832, Springer, Berlin, 1980, pp. 177–194. MR 607153
  • C. W. Curtis and G. I. Lehrer, Homology representations of finite groups of Lie type, Papers in algebra, analysis and statistics (Hobart, 1981) Contemp. Math., vol. 9, Amer. Math. Soc., Providence, R.I., 1981, pp. 1–28. MR 655971
  • C. W. Curtis, G. I. Lehrer, and J. Tits, Spherical buildings and the character of the Steinberg representation, Invent. Math. 58 (1980), no. 3, 201–210. MR 571572, DOI 10.1007/BF01390251
  • Howard Garland, $p$-adic curvature and the cohomology of discrete subgroups of $p$-adic groups, Ann. of Math. (2) 97 (1973), 375–423. MR 320180, DOI 10.2307/1970829
  • Louis Solomon, The Steinberg character of a finite group with $BN$-pair, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp. 213–221. MR 0246951
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 154-156
  • MSC: Primary 20G40; Secondary 20C15
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0652431-1
  • MathSciNet review: 652431