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2019

On generalized Macdonald polynomials

Mironov, A., Morozov, A.

Understand

Generalized Macdonald polynomials (GMP) are eigenfunctions of specifically-deformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials.

They are orthogonal with respect to a modified scalar product, which could be constructed with the help of an increasingly important triangular perturbation theory, showing up in a variety of applications.
A peculiar feature of GMP is that denominators in this expansion are fully factorized, which is a consequence of a hidden symmetry resulting from the special choice of the Hamiltonian deformation.
We introduce also a simplified but deformed version of GMP, which we call generalized Schur functions.

Built on

Y. Ohkubo, H. Awata, H. Fujino, arXiv:1512.08016 M. Fukuda, Y. Ohkubo, J. Shiraishi, arXiv:1903.05905
Original
1903
Earlier work this paper cites.
A. Mironov, A. Morozov, Nucl.Phys. B944
Original
1903
Earlier work this paper cites.
A. Mironov, A. Morozov, S. Natanzon, Theor.Math.Phys. 166
Original
1904
Earlier work this paper cites.
H. Awata, H. Kanno, A. Mironov, A. Morozov, arXiv:1905.00208
Original
1905
Earlier work this paper cites.
A. Morozov, arXiv:1906.09971
Original
1906
Earlier work this paper cites.
R. de Mello Koch, S. Ramgoolam, arXiv:1002.1634 J. Ben Geloun, S. Ramgoolam, arXiv:1307.6490; arXiv:1806.01085 P. Diaz, S.J. Rey, arXiv:1706.02667, arXiv:1801.10506 R. de Mello Koch, D. Gossman, L. Tribelhorn, JHEP 2017
Original
1907
Earlier work this paper cites.
S.N.M. Ruijsenaars, H. Schneider, Ann.Phys. (NY), 170
1988
Earlier work this paper cites.
S.V. Kerov, Func.An.and Apps. 25
1991
Earlier work this paper cites.
P.G.O. Freund, A.V. Zabrodin, Phys.Lett. B294
1992
Earlier work this paper cites.

Similar

I.G. Macdonald, Symmetric functions and Hall polynomials
1995
Cited alongside, same era.
Vl. Dotsenko, V. Fateev, Nucl. Phys. B240
1995
Cited alongside, same era.
N. Nekrasov, Adv. Theor. Math. Phys. 7
2003
Cited alongside, same era.
P. Biane, in: Asymptotic Combinatorics with Applications to Mathematical Physics,
2003
Cited alongside, same era.
J. Ding, K. Iohara, Lett.Math.Phys. 41
2007
Cited alongside, same era.
R. Dijkgraaf, C. Vafa, arXiv:0909.2453 H. Itoyama, K. Maruyoshi, T. Oota, Prog. Theor. Phys. 123
Original
2010
Cited alongside, same era.