Scattering matrices and affine Hecke algebras

Abstract

We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke algebras coincides with commuting Hamiltonians. These Hamiltonians have q-deformed affine Lie algebras as symmetry algebra.

22 pages, harvmac, no figures, Lecture at Schladming, March 4,11 1995

References in corpus (2)

• Yang-Baxter equation in spin chains with long range interactions
• A lecture on the Calogero-Sutherland models

Cited by in corpus (2)

• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials