28 citations · 117 across the 14 of their papers we have counts for
18 papers
Baxter -operator for the hyperbolic Calogero--Moser system
Martin Hallnäs
We introduce a -operator for the hyperbolic Calogero--Moser system as a one-parameter family of explicit integral operators. We establish the standard properties…
New orthogonality relations for super-Jack polynomials and an associated Lassalle--Nekrasov correspondence
Martin Hallnäs
The super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are polynomials in variables, which reduce to the Jack polynomials when or and provide jo…
Higher order deformed elliptic Ruijsenaars operators
Martin Hallnäs, Edwin Langmann, Masatoshi Noumi +1
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of oper…
From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators
Martin Hallnäs, Edwin Langmann, Masatoshi Noumi +1
Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with -type root systems of different ranks. By multiple…
Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
Farrokh Atai, Martin Hallnäs, Edwin Langmann
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctio…
Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems
Tamás F. Görbe, Martin A. Hallnäs
Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider -particle systems, with phase space symplectomorp…
On the Spectra of Real and Complex Lamé Operators
William A. Haese-Hill, Martin A. Hallnäs, Alexander P. Veselov
We study Lamé operators of the form with and a half-period of . For rectangular period lattices, we c…
Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. II. The two- and three-variable cases
Martin Hallnäs, Simon Ruijsenaars
In a previous paper we introduced and developed a recursive construction of joint eigenfunctions for the Hamiltonians of the hyperbolic relativistic Calogero-M…
Complex exceptional orthogonal polynomials and quasi-invariance
William A. Haese-Hill, Martin A. Hallnäs, Alexander P. Veselov
Consider the Wronskians of the classical Hermite polynomials where $k_i=λ_i+n-i,…
Product formulas for the relativistic and nonrelativistic conical functions
Martin Hallnäs, Simon Ruijsenaars
The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its rela…
A product formula for the eigenfunctions of a quartic oscillator
Martin Hallnäs, Edwin Langmann
We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type $ψ_k(x)ψ_k(y) = \int_{\mathbb{R}} ψ_k(z)\math…
Source identities and kernel functions for deformed (quantum) Ruijsenaars models
F. Atai, M. Hallnäs, E. Langmann
We consider the relativistic generalization of the quantum Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic…
A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians
Martin Hallnäs, Simon Ruijsenaars
We obtain symmetric joint eigenfunctions for the commuting PDOs associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion sc…
Baker-Akhiezer functions and generalised Macdonald-Mehta integrals
M. V. Feigin, M. A. Hallnas, A. P. Veselov
For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a genera…
Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. I. First steps
Martin Hallnäs, Simon Ruijsenaars
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyp…
Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
Martin Hallnäs, Simon Ruijsenaars
We obtain kernel functions associated with the quantum relativistic Toda systems, both for the periodic version and for the nonperiodic version with its dual. This involves taking…
A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
Martin Hallnäs, Edwin Langmann
In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cas…
Explicit formulas for the eigenfunctions of the N-body Calogero model
Martin Hallnäs, Edwin Langmann
We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two…