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), 3983-4021
MSC:
Primary 20D06; Secondary 17B20, 22E60
DOI:
https://doi.org/10.1090/S0002-9947-1995-1308021-4
MathSciNet review:
1308021
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.
- [1] T. Brocker and T. tom Dieck, Representations of compact Lie groups, Springer-Verlag, 1985. MR 781344 (86i:22023)
- [2]
A. M. Cohen and D. B. Wales, Finite subgroups of
, Comm. Algebra 11 (1983), 441-459. MR 689418 (85b:20010)
- [3]
-, Finite subgroups of
and
, preprint, 1992.
- [4] -, Finite simple subgroups of semisimple complex Lie groups--a 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), 1889-1907. 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, Springer-Verlag, 1972. MR 0323842 (48:2197)
- [9] Kenneth Ireland and Michael Rosen, A classical introduction to modern number theory, Springer-Verlag, 1990. MR 1070716 (92e:11001)
- [10]
Peter B. Kleidman and A. J. E. Ryba, Kostant's conjecture holds for
, J. Algebra 161 (1993), 535-540. 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), 973-1032. 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, Springer-Verlag, 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.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 20D06, 17B20, 22E60
Retrieve articles in all journals with MSC: 20D06, 17B20, 22E60
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1995-1308021-4
Keywords:
,
,
Kostant's conjecture
Article copyright:
© Copyright 1995
American Mathematical Society