Geodesic
The combinatorics of orbital varieties closures of nilpotent order 2 in \(\text{sl}_ n\)
The electronic journal of combinatorics, Tome 12 (2005)
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We consider two partial orders on the set of standard Young tableaux. The first one is induced to this set from the weak right order on symmetric group by Robinson-Schensted algorithm. The second one is induced to it from the dominance order on Young diagrams by considering a Young tableau as a chain of Young diagrams. We prove 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 special linear algebra $sl_n.$
DOI : 10.37236/1918
Classification : 05E10, 17B10
Mots-clés : Young tableaux, partial orders, Robinson-Schensted algorithm 
@article{10_37236_1918,
     author = {Anna Melnikov},
     title = {The combinatorics of orbital varieties closures of nilpotent order 2 in \(\text{sl}_ n\)},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1918},
     zbl = {1083.05041},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1918/}
}
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Anna Melnikov. The combinatorics of orbital varieties closures of nilpotent order 2 in \(\text{sl}_ n\). The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1918

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