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Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

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posted on 21.07.2014 by Mikhail V. Feigin, Martin Hallnas, Alexander Veselov
For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian function with respect to the Fourier transformation. We show that the value of properly normalised Baker-Akhiezer function at the origin can be given by an integral of Macdonald-Mehta type and explicitly compute these integrals for all known Baker-Akhiezer arrangements. We use the Dotsenko-Fateev integrals to extend this calculation to all deformed root systems, related to the non-exceptional basic classical Lie superalgebras.

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School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF MATHEMATICAL PHYSICS

Volume

54

Issue

5

Pages

? - ? (22)

Citation

FEIGIN, M.V., HALLNAS, M. and VESELOV, A.P., 2013. Baker-Akhiezer functions and generalised Macdonald-Mehta integrals. Journal of Mathematical Physics, 54 (5), 052106.

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© AIP Publishing LLC

Version

VoR (Version of Record)

Publication date

2013

Notes

Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics, 54 (5), 052106 and may be found at http://dx.doi.org/10.1063/1.4804615.

ISSN

0022-2488

Language

en

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