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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 $sl_n.$

The Combinatorics of Orbital Varieties Closures of Nilpotent Order 2 in sl${}_n$