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).
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