Generalized Macdonald-Ruijsenaars systems

@article{Feigin2011GeneralizedMS,
  title={Generalized Macdonald-Ruijsenaars systems},
  author={Misha Feigin and Alexey Silantyev},
  journal={arXiv: Quantum Algebra},
  year={2011}
}
View PDF on arXiv
9 Citations
Background Citations
1

9 Citations

Citation Type

Citation Type

Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed…
From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his…
This is a repository copy of Orthogonality relations and Cherednik identities for multivariable
We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these…
Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions
Higher Order Deformed Elliptic Ruijsenaars Operators
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was…
A bispectral q-hypergeometric basis for a class of quantum integrable models
For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the…
Quantum Lax Pairs via Dunkl and Cherednik Operators
  • O. Chalykh
  • Mathematics, Physics
    Communications in Mathematical Physics
  • 2019
We establish a direct link between Dunkl operators and quantum Lax matrices $${{\mathcal{L}}}$$L for the Calogero–Moser systems associated to an arbitrary Weyl group W (or an arbitrary finite…
Source Identities and Kernel Functions for the Deformed Koornwinder–van Diejen Models
We consider generalizations of the BC -type relativistic Calogero–Moser–Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornwinder and van…
Eigenfunctions of the van Diejen model generated by gauge and integral transformations
We present how explicit eigenfunctions of the principal Hamiltonian for the BCm relativistic Calogero-Moser-Sutherland model, due to van Diejen, can be constructed using gauge and integral…

References

SHOWING 1-10 OF 41 REFERENCES
Nonsymmetric Koornwinder polynomials and duality
In the fundamental work of Lusztig [L] on affine Hecke algebras, a special role is played by the root system of type Cn. The affine Hecke algebra is a deformation of the group algebra of an affine…
Lectures on affine Hecke algebras and Macdonald’s conjectures
This paper gives a review of Cherednik’s results on the representation-theoretic approach to Macdonald polynomials and related special functions. Macdonald polynomials are a remarkable 2-parameter…
On unitary submodules in the polynomial representations of rational Cherednik algebras
We consider representations of rational Cherednik algebras which are particular ideals in the ring of polynomials. We investigate convergence of the integrals which express the Gaussian inner product…
Generalized Calogero–Moser systems from rational Cherednik algebras
We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals that are invariant under the action of the…
Nonsemisimple Macdonald polynomials
Abstract.The paper is mainly devoted to the irreducibility of the polynomial representation of the double affine Hecke algebra for an arbitrary reduced root system and generic “central charge” q. The…
BC∞ Calogero–Moser operator and super Jacobi polynomials
Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials
It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald- Ruijsenaars operator in infinite number of…
Subrepresentations in the Polynomial Representation of the Double Affine Hecke Algebra of type $GL_n
We study a Laurent polynomial representation $V$ of the double affine Hecke algebra of type $GL_n$ for specialized parameters $t^{k+1}q^{r-1}=1$. We define a series of subrepresentations of $V$ by…
Macdonald Polynomials and Algebraic Integrability
We construct explicitly (nonpolynomial) eigenfunctions of the difference operators by Macdonald in the case t=qk, k∈Z. This leads to a new, more elementary proof of several Macdonald conjectures,…
Double affine Hecke algebras and Macdonald's conjectures
In this paper we prove the main results about the structure of double affine Hecke algebras announced in [C1], [C2]. The technique is based on the realization of these algebras in terms of…
...
...