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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On actions of adjoint type on complex Stiefel manifolds
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by McKenzie Y. Wang PDF
Trans. Amer. Math. Soc. 272 (1982), 611-628 Request permission

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
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 611-628
  • MSC: Primary 57S15; Secondary 57S25
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662056-4
  • MathSciNet review: 662056