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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Abstract
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 |
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| 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 http://dx.doi.org/10.1063/1.4804615</p> |
| Status: | Published |
| Refereed: | Yes |
| 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 |
| ISSN: | 0022-2488 |
| 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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