62 citations · 222 across the 14 of their papers we have counts for
7 papers · 1 filter
Quantum Lax pairs via Dunkl and Cherednik operators
Oleg Chalykh
We establish a direct link between Dunkl operators and quantum Lax matrices for the Calogero--Moser systems associated to an arbitrary Weyl group (or an arbitrary…
KP hierarchy for the cyclic quiver
Oleg Chalykh, Alexey Silantyev
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra . This hierarchy depends on parameters (one…
Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions
Oleg Chalykh, Pavel Etingof
We establish orthogonality relations for the Baker-Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik-Macdonald-Mehta integra…
Bethe Ansatz for the Ruijsenaars Model of BC_1-Type
Oleg Chalykh
We consider one-dimensional elliptic Ruijsenaars model of type . It is given by a three-term difference Schrödinger operator containing 8 coupling constants. We show that…
-modules and Calogero-Moser Spaces
Yuri Berest, Oleg Chalykh
We re-examine the bijective correspondence between the set of isomorphism classes of ideals of the first Weyl algebra and associated quiver varieties (Calogero-Moser spaces) \cite{…
Macdonald polynomials and algebraic integrability
Oleg Chalykh
We construct explicitly non-polynomial eigenfunctions of the difference operators by Macdonald in case , . This leads to a new, more elementary proof of sev…