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arXiv · 0804.0046

Trigonometric Cherednik algebra at critical level and quantum many-body problems

E. Emsiz·E. M. Opdam·J. V. Stokman
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Abstract

For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra $A(k)$ at critical level in terms of Dunkl type operators. Under this representation the center of $A(k)$ produces quantum conserved integrals for root system generalizations of quantum spin-particle systems on the circle with delta function interactions. This enables us to translate the spectral problem of such a quantum spin-particle system to questions in the representation theory of $A(k)$. We use this approach to derive the associated Bethe ansatz equations. They are expressed in terms of the normalized intertwiners of $A(k)$.

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BibTeXRIS

E. Emsiz, E. M. Opdam, J. V. Stokman. 2008-04-01. Trigonometric Cherednik algebra at critical level and quantum many-body problems. https://doi.org/10.1007/s00029-009-0516-y

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