A Hierarchical Array of Integrable Models

Details A Hierarchical Array of Integrable Models A Hierarchical Array of Integrable Models

1992-08-12

arxiv.org/abs/hep-th/9208033v1

J.Math.Phys. 34 (1993) 5832-5842

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, EFI-92-29

Scientific paper

10.1063/1.530285

Motivated by Harish-Chandra theory, we construct, starting from a simple CDD\--pole $S$\--matrix, a hierarchy of new $S$\--matrices involving ever ``higher'' (in the sense of Barnes) gamma functions.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. In setting up this array we were led to new results on the $q$\--gamma function and on the $q$\--deformed Bloch\--Wigner function.

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