Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

Feigin, M.V. , Hallnäs, M.A. and Veselov, A.P. (2013) Baker-Akhiezer functions and generalised Macdonald-Mehta integrals. Journal of Mathematical Physics, 54(5), 052106. (doi: 10.1063/1.4804615)

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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.

Item Type:Articles
Additional Information:<p>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</p> <p>The following article appeared in Journal of Mathematical Physics 54(5):052106 and may be found at</p>
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M.V., Hallnäs, M.A., and Veselov, A.P.
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Journal of Mathematical Physics
Publisher:American Institute of Physics
Copyright Holders:Copyright © 2013 AIP Publishing LLC
First Published:First published in Journal of Mathematical Physics 54(5):052106
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
569301From elliptic systems to Frobenius manifolds - 6d theories and AGTMikhail FeiginRoyal Society (ROYSOC)JP101196M&S - MATHEMATICS