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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. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
  • [2] M. F. Atiyah, 𝐾-theory, Lecture notes by D. W. Anderson, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0224083
  • [3] Raoul Bott, The index theorem for homogeneous differential operators, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 167–186. MR 0182022
  • [4] Jack M. Shapiro, A duality theorem for the representation ring of a compact connected Lie group, Illinois J. Math. 18 (1974), 79–106. MR 0339173
  • [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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