Finite-difference representations of the degenerate affine Hecke algebra

Abstract

The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The $sl(m)$-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebra are shown to be related to the Yangian representation of the 1-d Hubbard Model.

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References in corpus (4)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• The Yangian symmetry of the Hubbard Model
• Density Correlation Functions in Calogero Sutherland Models

Cited by in corpus (3)

• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials
• Bethe ansatz inside Calogero-Sutherland models