JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 2, Pages 157 - 186
(February 2020) http://dx.doi.org/10.17654/NT045020157 |
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CORRESPONDENCE BETWEEN ORBITAL VARIETIES AND SETS OF SUBSPACES STABLE UNDER NILPOTENT ENDOMORPHISM
Takashi Maeda
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Abstract: From the bijective correspondence between standard tableaux T of shape λ and left LR (Littlewood-Richardson) words L of weight (conjugate of λ), we show that generic points of orbital variety and set of subspaces stable under a nilpotent linear endomorphism describe each other. Here, is the word tableau associated to L. As a result, orderings defined by inclusions of closures correspond (Theorem A). |
Keywords and phrases: Jordan type, orbital variety, Littlewood-Richardson tableau.
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