C. Berg, N. Bergeron, H. Thomas, H. , and M. Zabrocki, Expansion of $k$-Schur functions for maximal rectangles within the affine nilCoxeter algebra, Journal of Combinatorics, vol.3, issue.3, pp.563-589, 2012.
DOI : 10.4310/JOC.2012.v3.n3.a9

A. Berenstein, S. Fomin, and A. Zelevinsky, Parametrizations of Canonical Bases and Totally Positive Matrices, Advances in Mathematics, vol.122, issue.1, pp.49-149, 1996.
DOI : 10.1006/aima.1996.0057

S. Fomin and A. Zelevinsky, Total Positivity: Tests and Parametrizations, The Mathematical Intelligencer, vol.2, issue.1, pp.23-33, 2000.
DOI : 10.1007/BF02786969
URL : http://arxiv.org/pdf/math/9912128

S. V. Kerov, Asymptotic representation theory of the symmetric group and its applications in analysis, AMS Translation of Mathematical Monographs, vol.219, 2003.

T. Lam, Affine Stanley symmetric functions, American Journal of Mathematics, vol.128, issue.6, pp.1553-1586, 2006.
DOI : 10.1353/ajm.2006.0045
URL : http://arxiv.org/pdf/math/0501335

T. Lam, The shape of a random affine Weyl group element and random core partitions, The Annals of Probability, vol.43, issue.4, pp.1643-1662, 2015.
DOI : 10.1214/14-AOP915

L. Lapointe, A. Lascoux, and J. Morse, Tableaux atoms and a new Macdonald positivity conjecture, Duke Math, vol.116, issue.1, pp.103-146, 2003.

C. Lecouvey, E. Lesigne, and M. Peigné, Conditioned random walks from Kac-Moody root systems, Transactions of the American Mathematical Society, vol.368, issue.5, pp.3177-3210, 2016.
DOI : 10.1090/tran/6468
URL : https://hal.archives-ouvertes.fr/hal-00833657

C. Lecouvey and P. Tarrago, Harmonic functions on multiplicative graphs and weight polytopes of representations

I. G. Macdonald, Symmetric functions, 1998.
DOI : 10.1090/ulect/012/01

J. Morse and A. Schilling, Crystal Approach to Affine Schubert Calculus, International Mathematics Research Notices, vol.21, issue.1, pp.2239-2294, 2016.
DOI : 10.1007/BF01466725
URL : http://arxiv.org/pdf/1408.0320

N. O. Connell, A path-transformation for random walks and the Robinson-Schensted correspondence, Transactions of the American Mathematical Society, vol.355, issue.09, pp.3669-3697, 2003.
DOI : 10.1090/S0002-9947-03-03226-4
URL : https://hal.archives-ouvertes.fr/hal-00136429

K. Rietsch, Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties, JAMS, vol.16, issue.2, pp.363-392, 2002.