, We see that all the properties are satisfied and thus that m ? ? ?s (O(s, ?)), the associated 3-partition is
On the product of two basic representations of Uv( sle), Adv. in Math, vol.218, pp.28-86, 2008. ,
Combinatorics of Coxeter groups, Graduate Text in Math, 2005. ,
, Groupes et algèbres de Lie, vol.4, 1968.
, Colored five-vertex models and Demazure atoms, 2019.
, Crystal bases representations and combinatorics, 2017.
Une nouvelle formule des caractères, Bull. Sc. Math, vol.98, pp.163-172, 1974. ,
Some characterization of the Bruhat order on a Coxeter group, Inven. Math, vol.39, pp.187-198, 1977. ,
Core blocks of Ariki-Koike algebras, Journal of Algebraic Combinatorics, vol.26, pp.47-81, 2007. ,
Representation theory, Graduate Texts in Mathematics, 1996. ,
Representations of Hecke algebras at roots of unity. Algebra and Applications, vol.15, 2011. ,
Representation theory and invariants of the classical groups, 2003. ,
Crystals and coboundary categories, Duke Math. J, vol.132, pp.191-216, 2006. ,
Introduction to quantum groups and crystal bases, Graduate Studies in Mathematics, vol.42, 2000. ,
Crystal graphs of irreducible highest weight Uq( sle)-modules of level two and Uglov bipartitions, Journal of Algebraic Combinatorics, vol.27, pp.143-162, 2008. ,
Kleshchev multipartitions and extended Young diagrams, Advances in Mathematics, vol.339, pp.367-403, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01902974
Kashiwara and Zelevinsky involution in affine type A, Pacific J. Math, vol.243, pp.287-311, 2009. ,
Crystal isomorphisms for irreducible highest weight Uv( sle)-modules of higher level, Algebras and Representation theory, vol.13, pp.467-489, 2010. ,
, Cores of Ariki-Koike algebras
Infinite dimensional Lie algebras, 1989. ,
A definition of the crystal commutator using Kashiwara's involution, Journal of Algebraic Combinatorics, vol.29, pp.261-268, 2010. ,
Crystal base and Littelmann's refined Demazure character formula, Duke Math, vol.71, pp.839-858, 1993. ,
On crystal bases, Representations of groups, vol.16, pp.155-197, 1994. ,
, Bases cristallines des groupes quantiques, vol.9, 2002.
Crystals for the representations of the q-analogues of classical Lie algebras, Journal of Algebra, vol.165, pp.295-345, 1994. ,
Invariant theory and tableaux 125-144, IMA, Math. Appl, vol.19, 1998. ,
Ordering the symmetric group, Algebraic combinatorics and applications, 2001. ,
, , 2014.
Schensted-type correspondences and plactic monoids for types Bn and Dn, Journal of Algebraic Combinatorics, vol.18, pp.99-133, 2003. ,
Combinatorics of crystal graph for the root systems of type An, Bn, Cn, Dn and G2, Combinatorial aspect of integrable systems, MSJ Mem, vol.17, pp.11-41, 2007. ,
On the combinatorics of crystal graphs, I. Lusztig's involution, Adv. in Math, vol.211, pp.204-243, 2007. ,
A generalization of the alcove model and its applications, Journal of Algebraic Combinatorics, vol.41, pp.751-83, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01283126
A Littlewood-Richardson type rule for symmetrizable Kac-Moody algebras, Inventiones Mathematicae, vol.116, pp.329-346, 1994. ,
Crystal graphs and Young tableaux, Journal of Algebra, vol.175, pp.65-87, 1995. ,
Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc, vol.3, pp.447-498, 1990. ,
An Explicit Construction of Type A Demazure Atoms, Journal of Algebraic Combinatorics, vol.29, pp.295-313, 2009. ,
Semistandard tableaux for Demazure characters (key polynomials) and their atoms, Eur. J. Comb, vol.45, pp.172-184, 2015. ,
Symplectic keys and Demazure atoms in type C ,
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