On the variety of invariant subspaces of a finite-dimensional linear operator

Author:
Mark A. Shayman

Journal:
Trans. Amer. Math. Soc. **274** (1982), 721-747

MSC:
Primary 15A04; Secondary 14M15

DOI:
https://doi.org/10.1090/S0002-9947-1982-0675077-2

MathSciNet review:
675077

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Abstract: If is a finite-dimensional vector space over or and , the set of -dimensional -invariant subspaces is a compact subvariety of the Grassmann manifold , but it need not be a Schubert variety. We study the topology of . We reduce to the case where is nilpotent. In this case we prove that is connected but need not be a manifold. However, the subset of consisting of those subspaces with a fixed cyclic structure is a regular submanifold of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0675077-2

Keywords:
Invariant subspace,
Grassmann manifold,
Schubert variety

Article copyright:
© Copyright 1982
American Mathematical Society