Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A new proof of a theorem of Solomon-Tits

Authors: C. W. Curtis and G. I. Lehrer
Journal: Proc. Amer. Math. Soc. 85 (1982), 154-156
MSC: Primary 20G40; Secondary 20C15
MathSciNet review: 652431
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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, No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • [2] Glen E. Bredon, Introduction to compact transformation groups, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 46. MR 0413144
  • [3] 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
  • [4] 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
  • [5] 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,
  • [6] Howard Garland, 𝑝-adic curvature and the cohomology of discrete subgroups of 𝑝-adic groups, Ann. of Math. (2) 97 (1973), 375–423. MR 0320180,
  • [7] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20G40, 20C15

Retrieve articles in all journals with MSC: 20G40, 20C15

Additional Information

Keywords: Tits system, combinatorial building, Coxeter complex, homology representation
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society