Séminaire Lotharingien de Combinatoire, 84B.49 (2020), 12 pp.

Joâo Miguel Santos

Symplectic Keys and Demazure Atoms in Type C

Abstract. We compute, mimicking the Lascoux-Sch\"utzenberger type A combinatorial procedure, left and right keys for a Kashiwara-Nakashima tableau in type C. These symplectic keys have a role similar to the keys for semistandard Young tableaux. More precisely, our symplectic keys give a tableau criterion for the Bruhat order on the hyperoctahedral group and cosets, and describe Demazure atoms and characters in type C. The right and the left symplectic keys are related through the Lusztig involution. A type C Schützenberger evacuation is defined to realize that involution.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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