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Proceedings of the American Mathematical Society

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



Conditions on a compact connected Lie group which insure a ``Weyl character formula''

Author: Jack M. Shapiro
Journal: Proc. Amer. Math. Soc. 51 (1975), 15-18
MSC: Primary 22E45; Secondary 55A10
MathSciNet review: 0367117
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Abstract: A theorem showing the equivalence of three conditions on a compact connected Lie group is proved. Among the corollaries is an extended ``Weyl character formula'' as originally stated by Bott.

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

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  • [2] M. F. Atiyah, $ K$-theory, Benjamin, New York, 1967. MR 36 #7130. MR 0224083 (36:7130)
  • [3] R. Bott, The index theorem for homogeneous differential operators, Differential and Combinatorial Topology (A Sympos. in Honor of Marston Morse), Princeton Univ. Press, Princeton, N. J., 1965, pp. 167-186. MR 31 #6246. MR 0182022 (31:6246)
  • [4] J. Shapiro, A duality theorem for the representation ring of a compact connected Lie group, Illinois J. Math. 18 (1974), 79-106. MR 0339173 (49:3936)
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  • [6] A. T. Vasquez, A Poincaré duality theorem for the equivariant $ K$-theory of homogenous spaces (preprint).

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Keywords: Weyl group, roots, weights, fundamental group
Article copyright: © Copyright 1975 American Mathematical Society

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