Geodesic
Symplectic keys and Demazure atoms in type \(C\)
João Miguel Santos1
1University of Coimbra
The electronic journal of combinatorics, Tome 28 (2021) no. 2
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We compute, mimicking the Lascoux-Schützenberger 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 Schützenberger evacuation is defined to realize that involution.
DOI : 10.37236/9235
Classification : 05E10, 05E05, 17B37
Mots-clés : Lascoux-Schützenberger type A combinatorial procedure, semistandard Young tableaux

João Miguel Santos  1

1 University of Coimbra 
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     author = {Jo\~ao Miguel Santos},
     title = {Symplectic keys and {Demazure} atoms in type {\(C\)}},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {2},
     doi = {10.37236/9235},
     zbl = {1465.05193},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9235/}
}
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João Miguel Santos. Symplectic keys and Demazure atoms in type \(C\). The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9235

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