Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On actions of adjoint type on complex Stiefel manifolds


Author: McKenzie Y. Wang
Journal: Trans. Amer. Math. Soc. 272 (1982), 611-628
MSC: Primary 57S15; Secondary 57S25
MathSciNet review: 662056
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G(m)$ denote $ {\rm {SU}}(m)$ or $ {\rm {Sp}}(m)$. It is shown that when $ m \geq 5\,G(m)$ cannot act smoothly on $ W_{n,2}$, the complex Stiefel manifold of orthonormal $ 2$-frames in $ \mathbf C^n$, for $ n$ odd, with connected principal isotropy type equal to the class of maximal tori in $ G(m)$. This demonstrates an important difference between $ W_{n,2}$, $ n$ odd, and $ S^{2n-3}\times S^{2n-1}$ in the behavior of differentiable transformation groups. Exactly the same holds for $ {\rm {SO}}(m)$ or Spin$ (m)$ if it is further assumed that a maximal $ 2$-torus of $ {\rm {SO}}(m)$ has fixed points.$ ^{2}$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S15, 57S25

Retrieve articles in all journals with MSC: 57S15, 57S25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0662056-4
PII: S 0002-9947(1982)0662056-4
Keywords: Stiefel manifolds, compact differentiable transformation groups, Steenrod operations, actions of adjoint type
Article copyright: © Copyright 1982 American Mathematical Society