Realizations of affine Weyl group symmetries on the quantum Painleve equations by fractional calculus

Nagoya, Hajime

doi:10.1007/s11005-012-0557-6

Realizations of affine Weyl group symmetries on the quantum Painleve equations by fractional calculus

Hajime Nagoya
(
- Kobe U.
)

2012

25 pages

Published in:

Lett.Math.Phys. 102 (2012) 297-321

DOI:

10.1007/s11005-012-0557-6

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Abstract: (Springer)

We realize affine Weyl group symmetries on the Schroedinger equations for the quantum Painleve equations, by fractional calculus. This realization enables us to construct an infinite number of hypergeometric solutions to the Schroedinger equations for the quantum Painleve equations. In other words, since the Schroedinger equations for the quantum Painleve equations are equivalent to the Knizhnik-Zamolodchikov equations, we give one method of constructing hypergeometric solutions to the Knizhnik-Zamolodchikov equations.

affine Weyl groups
quantum Painleve equations
Knizhnik-Zamolodchikov equations
hypergeometric integrals

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