Combinatorics/Lie algebras
The flush statistic on semistandard Young tableaux
[La statistique alignée sur des tableaux de Young semi-standard]
Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 367-371.

Dans cette note est définie une statistique sur les tableaux de Young, encodant les données nécessaires à la formule de Casselman–Shalika.

In this note, a statistic on Young tableaux is defined, which encodes data needed for the Casselman–Shalika formula.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.03.007
Salisbury, Ben 1

1 Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, United States
@article{CRMATH_2014__352_5_367_0,
     author = {Salisbury, Ben},
     title = {The flush statistic on semistandard {Young} tableaux},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {367--371},
     publisher = {Elsevier},
     volume = {352},
     number = {5},
     year = {2014},
     doi = {10.1016/j.crma.2014.03.007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2014.03.007/}
}
TY  - JOUR
AU  - Salisbury, Ben
TI  - The flush statistic on semistandard Young tableaux
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 367
EP  - 371
VL  - 352
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2014.03.007/
DO  - 10.1016/j.crma.2014.03.007
LA  - en
ID  - CRMATH_2014__352_5_367_0
ER  - 
%0 Journal Article
%A Salisbury, Ben
%T The flush statistic on semistandard Young tableaux
%J Comptes Rendus. Mathématique
%D 2014
%P 367-371
%V 352
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2014.03.007/
%R 10.1016/j.crma.2014.03.007
%G en
%F CRMATH_2014__352_5_367_0
Salisbury, Ben. The flush statistic on semistandard Young tableaux. Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 367-371. doi : 10.1016/j.crma.2014.03.007. http://www.numdam.org/articles/10.1016/j.crma.2014.03.007/

[1] Beineke, J.; Brubaker, B.; Frechette, S. Weyl group multiple Dirichlet series of type C, Pac. J. Math., Volume 254 (2011) no. 1, pp. 11-46

[2] Beineke, J.; Brubaker, B.; Frechette, S. A crystal definition for symplectic multiple Dirichlet series, Multiple Dirichlet Series, L-Functions and Automorphic Forms, Prog. Math., vol. 300, Birkhäuser/Springer, New York, 2012, pp. 37-63

[3] Brubaker, B.; Bump, D.; Friedberg, S. Weyl group multiple Dirichlet series, Eisenstein series and crystal bases, Ann. Math. (2), Volume 173 (2011) no. 1, pp. 1081-1120

[4] Brubaker, B.; Bump, D.; Friedberg, S. Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory, Ann. Math. Stud., vol. AM-175, Princeton Univ. Press, New Jersey, 2011

[5] Bump, D.; Nakasuji, M. Integration on p-adic groups and crystal bases, Proc. Am. Math. Soc., Volume 138 (2010) no. 5, pp. 1595-1605

[6] Chinta, G.; Gunnells, P.E. Littelmann patterns and Weyl group multiple Dirichlet series of type D, Multiple Dirichlet Series, L-Functions and Automorphic Forms, Prog. Math., vol. 300, Birkhäuser/Springer, New York, 2012, pp. 119-130

[7] Friedberg, S.; Zhang, L. Eisenstein series on covers of odd orthogonal groups | arXiv

[8] Friedlander, H.; Gaudet, L.; Gunnells, P.E. Crystal graphs, Tokuyama's theorem, and the Gindikin–Karpelevič formula for G2 | arXiv

[9] Hong, J.; Kang, S.-J. Introduction to Quantum Groups and Crystal Bases, Grad. Stud. Math., vol. 42, American Mathematical Society, Providence, RI, 2002

[10] Hong, J.; Lee, H. Young tableaux and crystal B() for finite simple Lie algebras, J. Algebra, Volume 320 (2008), pp. 3680-3693

[11] Kashiwara, M. On crystal bases, Banff, AB, 1994 (CMS Conf. Proc.), Volume vol. 16, Amer. Math. Soc., Providence, RI (1995), pp. 155-197

[12] Kim, H.H.; Lee, K.-H. Representation theory of p-adic groups and canonical bases, Adv. Math., Volume 227 (2011) no. 2, pp. 945-961

[13] Kim, H.H.; Lee, K.-H. Quantum affine algebras, canonical bases, and q-deformation of arithmetical functions, Pac. J. Math., Volume 255 (2012) no. 2, pp. 393-415

[14] Lee, K.-H.; Lombardo, P.; Salisbury, B. Combinatorics of the Casselman–Shalika formula in type A, Proc. Am. Math. Soc. (2014) (in press) | arXiv | DOI

[15] Lee, K.-H.; Salisbury, B. A combinatorial description of the Gindikin–Karpelevich formula in type A, J. Comb. Theory, Ser. A, Volume 119 (2012), pp. 1081-1094

[16] Lee, K.-H.; Salisbury, B. Young tableaux, canonical bases, and the Gindikin–Karpelevich formula, J. Korean Math. Soc., Volume 51 (2014) no. 2, pp. 289-309

[17] Tokuyama, T. A generating function of strict Gelfand patterns and some formulas on characters of general linear groups, J. Math. Soc. Jpn., Volume 40 (1988) no. 4, pp. 671-685

Cité par Sources :