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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Conditions on a compact connected Lie group which insure a “Weyl character formula”
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by Jack M. Shapiro PDF
Proc. Amer. Math. Soc. 51 (1975), 15-18 Request permission

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
  • J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
  • M. F. Atiyah, $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1967. Lecture notes by D. W. Anderson. MR 0224083
  • 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
  • Jack M. Shapiro, A duality theorem for the representation ring of a compact connected Lie group, Illinois J. Math. 18 (1974), 79–106. MR 339173
  • —, 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. A. T. Vasquez, A Poincaré duality theorem for the equivariant $K$-theory of homogenous spaces (preprint).
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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