Baker-Akhiezer functions and generalised Macdonald-Mehta integrals
نویسندگان
چکیده
منابع مشابه
Discrete analogues of Macdonald-Mehta integrals
Article history: Available online 15 July 2016
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A notion of rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in C is introduced. It is proved that BA function exists only for very special configurations (locus configurations), which satisfy certain overdetermined algebraic system. The BA functions satisfy some algebraically integrable Schrödinger equations, so any locus configuration determines such an equation...
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We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summati...
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with respect to the Gaussian measure. Macdonald extended it from An−1 to other root systems and verified his conjecture for classical ones by means of the Selberg integrals [M1]. It was established by Opdam in [O1] in full generality using the shift operators. The integral is an important normalization constant for a k-deformation of the Hankel transform introduced by Dunkl [D]. The generalized...
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We show here that a certain sequence of polynomials arising in the study of S2 m-quasi invariants satisfies a 3-term recursion. This leads to the discovery that these polynomials are closely related to the Bessel polynomials studied by Luc Favreau. This connection reveals a variety of combinatorial properties of the sequence of Baker–Akhiezer functions for S2. In particular we obtain in this ma...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2013
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4804615