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math.QA2022
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…
math.QA2021★ 1 cited
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…
math.QA2021★ 10 cited
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…