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Proceedings of the American Mathematical Society

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

 

 

Splitting universal bundles over flag manifolds


Author: R. E. Stong
Journal: Proc. Amer. Math. Soc. 84 (1982), 576-580
MSC: Primary 55R40; Secondary 57R15
DOI: https://doi.org/10.1090/S0002-9939-1982-0643753-9
MathSciNet review: 643753
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Abstract: Let $ {\mathbf{F}}$ be one of the fields $ {\mathbf{R}}$, $ {\mathbf{C}}$, or $ {\mathbf{H}}$ and correspondingly let $ {\mathbf{F}}G$ be $ O$, $ U$, or $ {\text{Sp}}$, i.e. the orthogonal, unitary, or symplectic group. Over the flag manifold $ {\mathbf{F}}G({n_1} + \cdots + {n_k})/{\mathbf{F}}G({n_1}) \times \cdots \times {\mathbf{F}}G({n_k})$ one has vector bundles $ {\gamma _i}$ over $ F$ of dimension $ {n_i}$, $ 1 \leqslant i \leqslant k$. This paper determines all cases in which $ {\gamma _i}$ decomposes nontrivially as a Whitney sum.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0643753-9
Article copyright: © Copyright 1982 American Mathematical Society