Work

Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

Year: 2013

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.4804615

Authors: M. V. Feigin, M. A. Hallnäs, A. P. Veselov

Institutions: University of Glasgow, Loughborough University, Lomonosov Moscow State University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Russian Foundation for Basic Research, Eidgenössische Technische Hochschule Zürich, Hausdorff Center for Mathematics, Engineering and Physical Sciences Research Council

Awards: G347999943, Symmetric Lie superalgebras and quantum integrability, G4929972126