On the variety of invariant subspaces of a finitedimensional linear operator
Author:
Mark A. Shayman
Journal:
Trans. Amer. Math. Soc. 274 (1982), 721747
MSC:
Primary 15A04; Secondary 14M15
MathSciNet review:
675077
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Abstract: If is a finitedimensional 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:
http://dx.doi.org/10.1090/S00029947198206750772
PII:
S 00029947(1982)06750772
Keywords:
Invariant subspace,
Grassmann manifold,
Schubert variety
Article copyright:
© Copyright 1982 American Mathematical Society
