Brauer diagrams, updown tableaux and nilpotent matrices

Terada, Itaru

Journal of Algebraic Combinatorics, Tome 14 (2001) no. 3, pp. 229-267.

Résumé

Summary: 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 $( N, w, V) (N,\omega ,V)$ where $V$ V is a complete flag in $\mathbb C ^{2 n}$ , w mathbbC^2n ,$\omega $ is a nondegenerate alternating bilinear form on $\mathbb C ^{2 n}$ mathbbC^2n and $N$ is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both $V$ V instead of Steinberg"s variety of ( $N, V, V$") (N,V,V") where $V and V$" V textand V" are two complete flags in $\mathbb C ^{ n}$ mathbbC^n and $N$ is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both $V and V$" V textand V" .

Détail

Keywords: Robinson-Schensted correspondence, Brauer algebra, Young diagram, nilpotent matrix, symplectic form