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A Unified Construction of Generalized Classical Polynomials Associated with Operators of Calogero–Sutherland Type

- Martin A. Hallnäs, E. Langmann
- Mathematics
- 30 March 2007

In this paper we consider a large class of many-variable polynomials which contains generalizations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur… Expand

Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators

- F. Atai, Martin A. Hallnäs, E. Langmann
- MathematicsBulletin of the London Mathematical Society
- 6 February 2018

We prove orthogonality and compute explicitly the (quadratic) norms for super‐Jack polynomials SPλ((z1,…,zn),(w1,…,wm);θ) with respect to a natural positive semi‐definite, but degenerate, Hermitian… Expand

Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation

- F. Atai, Martin A. Hallnäs, E. Langmann
- Mathematics
- 12 March 2021

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… Expand

An orthogonality relation for multivariable Bessel polynomials

- Martin A. Hallnäs
- Mathematics
- 18 September 2008

In a recent paper we introduced a multivariable generalization of the Bessel polynomials, depending on one extra parameter, and related to the so-called hyperbolic Calogero–Moser–Sutherland model… Expand

Quantum Calogero-Sutherland type models and generalised classical polynomials

- Martin A. Hallnäs, E. Langmann
- Mathematics
- 30 March 2007

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 cases, and which occ… Expand

Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

- F. Atai, Martin A. Hallnäs, E. Langmann
- Mathematics
- 18 November 2013

We consider the relativistic generalization of the quantum AN-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these… Expand

Complex Exceptional Orthogonal Polynomials and Quasi-invariance

- William A. Haese-Hill, Martin A. Hallnäs, A. Veselov
- Mathematics
- 23 September 2015

AbstractConsider the Wronskians of the classical Hermite polynomials
$$H_{\lambda, l}(x):=\mathrm{Wr}(H_l(x),H_{k_1}(x),\ldots,H_{k_n}(x)), \quad l \in \mathbb Z_{\geq0}{\setminus}… Expand

Higher Order Deformed Elliptic Ruijsenaars Operators

- Martin A. Hallnäs, E. Langmann, M. Noumi, H. Rosengren
- MathematicsCommunications in Mathematical Physics
- 6 May 2021

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… Expand

Multivariable Bessel Polynomials Related to the Hyperbolic Sutherland Model with External Morse Potential

- Martin A. Hallnäs
- Mathematics
- 29 July 2008

A multivariable generalization of the Bessel polynomials is introduced and studied. In particular, we deduce their series expansion in Jack polynomials, a limit transition from multivariable Jacobi… Expand

An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models

- Martin A. Hallnäs
- Mathematics
- 2007

We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero Sutherland type models. We al… Expand

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