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.

**[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 -theory of and*, Illinois J. Math.**18**(1974), 509-515.**[6]**A. T. Vasquez,*A Poincaré duality theorem for the equivariant -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