## Abstract

Motivated by Harish-Chandra theory, starting from a simple CDD-pole S matrix, a hierarchy of new S matrices involving ever "higher" (in the sense of Barnes) gamma functions are constructed. These new S matrices correspond to scattering of excitations in ever more complex integrable models. From each of these models, new ones are obtained either by "q deformation," or by considering the Selberg-type Euler products of which they represent the "infinite place." A hierarchic array of integrable models is thus obtained. A remarkable diagonal link in this array is established. Though many entries in this array correspond to familiar integrable models, the array also leads to new models. Setting up this array led to new results on the q-gamma function and on the q-deformed Bloch-Wigner function.

Original language | English |
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Pages (from-to) | 5832-5842 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 34 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |