Abstract
AbstractWe consider the generalised Calogero–Moser–Sutherland quantum integrable system associated to the configuration of vectors $$AG_2$$
A
G
2
, which is a union of the root systems $$A_2$$
A
2
and $$G_2$$
G
2
. We establish the existence of and construct a suitably defined Baker–Akhiezer function for the system, and we show that it satisfies bispectrality. We also find two corresponding dual difference operators of rational Macdonald–Ruijsenaars type in an explicit form.
Funder
Russian Science Foundation
Carnegie Trust for the Universities of Scotland
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Mathematical Physics
Reference30 articles.
1. Berezin, F.A., Pokhil, G.P., Finkelberg, V.M.: Schrödinger equation for a system of one-dimensional particles with point interaction. Vestnik Moskov. Univ. Ser. 1, 21–28 (1964)
2. Calogero, F.: Solution of the one-dimensional $$n$$-body problem with quadratic and/or inversely quadratic pair potential. J. Math. Phys. 12, 419–436 (1971)
3. Chalykh, O.A.: Darboux transformations for multidimensional Schrödinger operators. Russ. Math. Surv. 53(2), 167–168 (1998)
4. Chalykh, O.A.: Bispectrality for the quantum Ruijsenaars model and its integrable deformation. J. Math. Phys. 41(8), 5139–5167 (2000)
5. Chalykh, O.A.: Algebro-geometric Schrödinger operators in many dimensions. Philos. Trans. R. Soc. A 366, 947–971 (2008)