Brauer Diagrams, Updown Tableaux and Nilpotent Matrices
نویسنده
چکیده
We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both ω and V, instead of Steinberg’s variety of (N , V, V′) where V and V′ are two complete flags in Cn and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both V and V′.
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