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The combinatorics of orbital varieties closures of nilpotent order 2 in sl(n)

Anna Melnikov
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Abstract

We consider two partial orders on standard Young tableaux. The first one is induced from the weak right Bruhat order on symmetric group by Robinson-Schensted algorithm. The second one is induced from the order on Young diagrams by considering a Young tableau as a chain of Young diagrams. We show that these two orders of completely different nature coincide on the subset of Young tableaux with 2 columns or with 2 rows. This fact has very interesting geometric implications for orbital varieties of nilpotent order 2 in sl(n).

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Anna Melnikov. 2005-05-08. The combinatorics of orbital varieties closures of nilpotent order 2 in sl(n). https://arxiv.org/abs/math/0312332

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