@article{SIGMA_2015_11_a97,
author = {Alexei Borodin and Ivan Corwin and Daniel Remenik},
title = {A {Classical} {Limit} of {Noumi's} $q${-Integral} {Operator}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2015},
volume = {11},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a97/}
}
TY - JOUR AU - Alexei Borodin AU - Ivan Corwin AU - Daniel Remenik TI - A Classical Limit of Noumi's $q$-Integral Operator JO - Symmetry, integrability and geometry: methods and applications PY - 2015 VL - 11 UR - http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a97/ LA - en ID - SIGMA_2015_11_a97 ER -
Alexei Borodin; Ivan Corwin; Daniel Remenik. A Classical Limit of Noumi's $q$-Integral Operator. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a97/
[1] Abramowitz M., Stegun I. A., Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55, U.S. Government Printing Office, Washington, D.C., 1964 | MR
[2] Borodin A., Corwin I., Macdonald processes,, Probab. Theory Related Fields, 158 (2014), 225–400, arXiv: 1111.4408 | DOI | MR | Zbl
[3] Borodin A., Corwin I., Gorin V., Shakirov S., “Observables of Macdonald processes”, Trans. Amer. Math. Soc. (to appear) , arXiv: 1306.0659 | DOI
[4] Feigin B., Hashizume K., Hoshino A., Shiraishi J., Yanagida S., “A commutative algebra on degenerate ${\mathbb{CP}}^1$ and Macdonald polynomials”, J. Math. Phys., 50 (2009), 095215, 42 pp., arXiv: 0904.2291 | DOI | MR | Zbl
[5] Gerasimov A., Kharchev S., Lebedev D., Oblezin S., “On a Gauss–Givental representation of quantum Toda chain wave function”, Int. Math. Res. Not., 2006 (2006), 96489, 23 pp., arXiv: math.RT/0505310 | DOI | MR | Zbl
[6] Gerasimov A., Lebedev D., Oblezin S., “Baxter operator and Archimedean Hecke algebra”, Comm. Math. Phys., 284 (2008), 867–896, arXiv: 0706.3476 | DOI | MR | Zbl
[7] Gerasimov A., Lebedev D., Oblezin S., “On $q$-deformed ${\mathfrak{gl}}_{\ell+1}$-Whittaker function, III”, Lett. Math. Phys., 97 (2011), 1–24, arXiv: 0805.3754 | DOI | MR | Zbl
[8] Gerasimov A., Lebedev D., Oblezin S., “On a classical limit of $q$-deformed Whittaker functions”, Lett. Math. Phys., 100 (2012), 279–290, arXiv: 1101.4567 | DOI | MR | Zbl
[9] Givental A., “Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture”, Topics in Singularity Theory, Amer. Math. Soc. Transl. Ser. 2, 180, Amer. Math. Soc., Providence, RI, 1997, 103–115, arXiv: alg-geom/9612001 | MR | Zbl
[10] Macdonald I. G., Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979 | MR
[11] Noumi M., Sano A., An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A, in preparation
[12] O'Connell N., Seppäläinen T., Zygouras N., “Geometric RSK correspondence, Whittaker functions and symmetrized random polymers”, Invent. Math., 197 (2014), 361–416, arXiv: 1210.5126 | DOI | MR | Zbl
[13] Stade E., “Archimedean $L$-factors on ${\rm GL}(n)\times{\rm GL}(n)$ and generalized Barnes integrals”, Israel J. Math., 127 (2002), 201–219, arXiv: 1102.2457 | DOI | MR | Zbl