Symplectic Keys and Demazure Atoms in Type C

• Author(s): Santos, João Miguel
• Date: 2021
• Persistent ID: https://hdl.handle.net/10316/103872
• Origin: Estudo Geral - Universidade de Coimbra
• Project/scholarship: info:eu-repo/grantAgreement/other/null/PD/other
• Document Type: Journal article
• Language: English

Description

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 similar role as 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 Sch utzenberger evacuation is de ned to realize that involution.