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

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

2003-12-17

arxiv.org/abs/math/0312332v2

Electronic Journal of Combinatorics, vol. 12(1), 2005, R21

Mathematics

Representation Theory

20 pages

Scientific paper

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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