% This is an example bibliography file for FPSAC submissions. @article{Li, author = { Littelmann, P.}, journal = {Annals of Mathematics}, number = {3}, volume = {142}, pages = {499--525}, title = {Paths and Root Operators in Representation Theory}, doi = {https://doi.org/10.2307/2118553}, year = {1995}, } @article{BR, author = { Baik, J. and Rains, E. M.}, journal = {Duke Math. J.}, number = {109}, pages = {1--65}, title = {Algebraic aspects of increasing subsequences}, doi = {10.1215/S0012-7094-01-10911-3}, volume = {1}, year = {2001}, } @article{AGL, author = {Azenhas, O. and Gobet, T. and Lecouvey, C.}, journal = {Accepted in Tunisian Journal of Mathematics}, doi = {https://doi.org/10.48550/arXiv.2212.06587}, title = {Non symmetric Cauchy kernel, crystals and last passage percolation}, year = {2023}, } @article{AE, author = { Azenhas, O. and Emami, A.}, journal = {European Journal of Combinatorics}, number = {3}, pages = {16--441}, title = {An analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircases}, doi = {10.1016/j.ejc.2014.11.006}, volume = {46}, year = {2015}, } @article{Lam, author = {Lam, T. }, title = {Whittaker functions, geometric crystals, and quantum Schubert calculus}, journal ={Adv. Stud. Pure Math., Mathematical Society of Japan}, url = { https://doi.org/10.48550/arXiv.1308.5451}, year = {2016}, pages={211-250}, volume={71}, } @article{CK, author = { Choi, S-I. and Kwon, J-H.}, journal = {Algebras and Representation Theory}, number = {3}, pages = {16--441}, title = {Lakshmibai-Seshadri Paths and Non-Symmetric Cauchy Identity}, doi = {10.1007/s10468-017-9752-6}, volume = {21}, year = {2018}, } @article{AO2, author = { Azenhas, O. and Emami, E.}, journal = {Dynamics, Games and Science, CIM Series, Springer}, title = { Growth diagrams and non-symmetric Cauchy identities on NW (SE) near staircases}, doi = {10.1007/978-3-319-16118-1_4}, year = {2015}, } @article{LS, author = { Lascoux, L. and Sch\"utzenberger, M.-P.}, journal = {In Invariant theory and tableaux (Minneapolis, MN, 1988), IMA Vol. Math. Appl., Springer}, title = { Keys and standard bases}, year = {1990}, volume = {19}, pages = {125--144}, url={http://igm.univ-mlv.fr/~berstel/Schutzenberger/Travaux/A/1990-1KeysIMA.pdf}, } @article{KN, author = { Kashiwara, M. and Nakashima, T.}, journal = {J. of Algebra}, number = {165}, pages = {295--345}, title = {Crystals for the representations of the $q$-analogues of classical Lie algebras}, year = {1994}, doi={10.1006/jabr.1994.1114}, } @article{Mas, author = { Mason, S.}, journal = {Algebr. Comb.}, number = {29}, pages = {295--313}, title = {An Explicit Construction of Type A Demazure Atoms}, year = {2009}, doi={10.1007/s10801-008-0133-4}, } @article{BDS, author = { Baik, J. and Deift, P. and Suidan, T.}, journal = {Graduate Studies in Mathematics, AMS}, number = {172}, title = {Combinatorics and Random Matrix Theory}, year = {2016}, } @article{Fu, author = { Fulton, W.}, journal = {London Math. Society Student Texts, Cambridge University Press}, title = {Young Tableaux: With Applications to Representation Theory and Geometry}, year = {1997}, } @article{BumpSchilling2017, author = { Bump, D. and Schilling, A.}, journal = {World Scientific}, title = {Crystal Bases: Representations And Combinatorics}, year = {2017}, } @article{OK, author = {Okounkov, A.}, journal = {Selecta Math.}, number = {1}, pages = {57-81}, title = {Infinite wedge and random partitions}, volume = {7}, year = {2001}, doi={ 10.48550/arXiv.math/9907127}, } @article{joh, author = { Johansson, K.}, journal = {J. Math. Physics}, number = {2}, pages = {437-476}, title = {Shape fluctuations and random matrices}, volume = {209}, year = {2000}, } @article{kash, author={ Kashiwara, M.}, title= {On crystal bases}, journal={Representations of groups (Banff, AB, 1994), CMS Conf. Proc., Amer. Math. Soc., Providence, RI}, volume={16}, year={1995}, pages={155-197}, } @article{Sta, author = { Stanley, R.}, journal = {Cambridge University Press}, number = {2}, title = {Enumerative Combinatorics}, year = {2001}, } @misc{FMO, AUTHOR = {Feigin, E. and Makedonskyi, I. and Orr, D.}, TITLE = {Nonsymmetric q-Cauchy identity and representations of the Iwahori algebra}, EPRINT = { 2303.00241}, EPRINTTYPE ={arxiv}, YEAR = {2023}, } @article{Las2, author = { Lascoux, A.}, journal = {Studies in Memory of Issai Schur, Progress in Mathematics, Birkha\"{u}ser}, number = {210}, title = {Double Crystal Graphs}, year = {2003}, pages={95--114}, url={https://web.archive.org/web/20180223120439/http://phalanstere.univ-mlv.fr/~al/} } @article{BZ, author = { Bisi, E. and Zygouras, N.}, journal = {Adv. in Math.}, number = {404 B}, title = {Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation}, year = {2022}, doi={10.1016/j.aim.2022.108453} } @article{BZ1, author = { Bisi, E. and Zygouras, N.}, journal = {Transactions of the American Mathematical Society}, number = {12}, volume = {371}, title = {Point-to-line polymers and orthogonal Whittaker functions}, year = {2019}, doi = {10.1090/tran/7423}, } @article{NPS, author = { Nazarov, A. and Postnova, O. and Scrimshaw, T.}, journal = {J. Lond. Math. Soc.}, doi = { 10.1112/jlms.12813}, title = {Skew Howe duality and limit shapes of Young diagrams}, year = {2023}, } @article{Ye, author = { Yeliussizov, D. }, journal = {C. R. Math. Acad. Sci. Paris}, number = {358}, title = {Dual Grothendieck polynomials via last-passage percolation}, year = {2020}, pages = {497--503}, doi={10.5802/crmath.67}, } @article{MR4, author = {Corliss, J. J.}, title = {Upper limits to the real roots of a real algebraic equation}, journal = {Amer. Math. Monthly}, fjournal = {The American Mathematical Monthly}, volume = {46}, year = {1939}, pages = {334--338}, issn = {0002-9890}, mrclass = {09.0X}, mrnumber = {0000004}, mrreviewer = {O. Sz\'asz}, doi = {10.2307/2302887} }