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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
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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 $.

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  • [1] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4-6, Actualités Sci. Indust. No. 1337, Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [2] G. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972. MR 0413144 (54:1265)
  • [3] C. Curtis, Homology representations of finite groups, Lecture Notes in Math., vol. 832, Springer-Verlag, Berlin and New York, 1980 pp. 177-194. MR 607153 (82c:20090)
  • [4] C. Curtis and G. Lehrer, Homology representations of finite groups of Lie type (to appear). MR 655971 (83g:20042)
  • [5] C. Curtis, G. Lehrer and J. Tits, Spherical buildings and the character of the Steinberg representation, Invent. Math. 58 (1960), 201-210. MR 571572 (81f:20060)
  • [6] H. Garland, $ p$-adic curvature and the cohomology of discrete subgroups of $ p$-adic groups, Ann. of Math. (2) 97 (1973), 375-393. MR 0320180 (47:8719)
  • [7] L. Solomon, The Steinberg character of a finite group with a $ BN$-pair, Theory of Finite Groups, R. Brauer and C. H. Sah, Eds., Benjamin, New York, 1969, pp. 213-221. MR 0246951 (40:220)

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

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