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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…
math.QA2018★ 12 cited
Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
Farrokh Atai, Martin Hallnäs, Edwin Langmann
We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials with respect to a natural positive semi-d…