Quantum Painlevé Equations: from Continuous to Discrete

Details Quantum Painlevé Equations: from Continuous to Discrete Quantum Painlevé Equations: from Continuous to Discrete

2008-06-09

arxiv.org/abs/0806.1466v1

SIGMA 4 (2008), 051, 9 pages

Mathematics

Quantum Algebra

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2008.051

We examine quantum extensions of the continuous Painlev\'e equations,
expressed as systems of first-order differential equations for non-commuting
objects. We focus on the Painlev\'e equations II, IV and V. From their
auto-B\"acklund transformations we derive the contiguity relations which we
interpret as the quantum analogues of the discrete Painlev\'e equations.

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