and the rank two Lie groups: their construction in light of Kostant's conjecture
Author:
Mark R. Sepanski
Journal:
Trans. Amer. Math. Soc. 347 (1995), 39834021
MSC:
Primary 20D06; Secondary 17B20, 22E60
MathSciNet review:
1308021
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Abstract: This paper deals with certain aspects of a conjecture made by B. Kostant in 1983 relating the Coxeter number to the occurrence of the simple finite groups in simple complex Lie groups. A unified approach to Kostant's conjecture that yields very general results for the rank two case is presented.
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 [2]
 A. M. Cohen and D. B. Wales, Finite subgroups of , Comm. Algebra 11 (1983), 441459. MR 689418 (85b:20010)
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 , Finite subgroups of and , preprint, 1992.
 [4]
 , Finite simple subgroups of semisimple complex Lie groupsa survey, preprint, 1994.
 [5]
 Arjeh M. Cohen, Jr., Robert L. Griess, and Bert Lisser, The groups embeds in the Lie group of type , Comm. Algebra 21 (1993), 18891907. MR 1215552 (94m:20041)
 [6]
 J. H. Conway, R. T. Curtis, et al., Atlas of finite groups, Clarendon Press, Oxford, 1985. MR 827219 (88g:20025)
 [7]
 Larry Dornhoff, Group representation theory: Part A, Marcel Dekker, 1971. MR 0347959 (50:458a)
 [8]
 James E. Humphreys, Introduction to Lie algebras and representation theory, SpringerVerlag, 1972. MR 0323842 (48:2197)
 [9]
 Kenneth Ireland and Michael Rosen, A classical introduction to modern number theory, SpringerVerlag, 1990. MR 1070716 (92e:11001)
 [10]
 Peter B. Kleidman and A. J. E. Ryba, Kostant's conjecture holds for , J. Algebra 161 (1993), 535540. MR 1247371 (94k:20025)
 [11]
 Bertram Kostant, The principal dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 9731032. MR 0114875 (22:5693)
 [12]
 , A tale of two conjugacy classes, Colloquium Lecture of the Amer. Math. Soc., 1983.
 [13]
 A. Meurman, An embedding of in , Lie Algebras and Related Topics, Lecture Notes in Math., vol. 933, Springer, 1982. MR 675113 (84b:20046)
 [14]
 M. A. Naimark and A. I. Štern, Theory of group representations, SpringerVerlag, 1982. MR 793377 (86k:22001)
 [15]
 Mohammad Ali Najafi, Clifford algebra structure on the cohomology algebra of compact symmetric spaces, Master's thesis, MIT, February, 1979.
 [16]
 Mark R. Sepanski, and the rank two Lie groups: their construction, geometry, and invariants in light of Kostant's Conjecture, Ph.D. thesis, MIT, May, 1994.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199513080214
PII:
S 00029947(1995)13080214
Keywords:
,
,
Kostant's conjecture
Article copyright:
© Copyright 1995
American Mathematical Society
