%0 Journal Article %A Feigin, Mikhail V. %A Hallnas, Martin %A Veselov, Alexander %D 2014 %T Baker-Akhiezer functions and generalised Macdonald-Mehta integrals %U https://repository.lboro.ac.uk/articles/journal_contribution/Baker-Akhiezer_functions_and_generalised_Macdonald-Mehta_integrals/9389066 %2 https://repository.lboro.ac.uk/ndownloader/files/17002322 %K untagged %K Mathematical Sciences not elsewhere classified %X 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. %I Loughborough University