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It is known by K. Okamoto [7] that the fourth Painlevé equation has symmetries under the affine Weyl group of type A (1) 2 . In this paper we propose a new representation of the fourth Painlevé… (More)

We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogona-lity relations for non-symmetric and anti-symmetric… (More)

In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlevé equations, with a particular emphasis on the discrete Painlevé equations.… (More)

It can be applied consistently to an arbitrary rational function expressed as a ratio of two polynomials with positive real coefficients, in order to produce a combination of +, − and max (or min),… (More)

The Painlev e equations and their higher order generalizations of type A are discussed from the viewpoint of aane Weyl group symmetry with respect to the BB acklund transformations.

We give a birational realization of affine Weyl group of type A (1) m−1 × A (1) n−1. We apply this representation to construct some discrete integrable systems and discrete Painlevé equations. Our… (More)

- Masatoshi Noumi
- 2004