10 citations · 19 across the 5 of their papers we have counts for
8 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…