Splitting universal bundles over flag manifolds
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- by R. E. Stong PDF
- Proc. Amer. Math. Soc. 84 (1982), 576-580 Request permission
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.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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