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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0367117-7
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?)

  • [1] J. F. Adams, Lectures on Lie groups, Benjamin, New York, 1969. MR 40 #5780. MR 0252560 (40:5780)
  • [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)
  • [5] -, On the algebraic structure of the $ K$-theory of $ {G_2}/SU(3)$ and $ {F_4}/\operatorname{Spin} (9)$, Illinois J. Math. 18 (1974), 509-515.
  • [6] A. T. Vasquez, A Poincaré duality theorem for the equivariant $ K$-theory of homogenous spaces (preprint).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367117-7
Keywords: Weyl group, roots, weights, fundamental group
Article copyright: © Copyright 1975 American Mathematical Society

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