Brauer Diagrams, Updown Tableaux and Nilpotent Matrices |
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Authors: | Itaru Terada |
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Abstract: | 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
where
is a complete flag in
is a nondegenerate alternating bilinear form on
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both and
instead of Steinberg's variety of
where
are two complete flags in
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both
. |
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Keywords: | Robinson-Schensted correspondence Brauer algebra Young diagram nilpotent matrix symplectic form |
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