Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 132, 10 pages      arXiv:2008.06825
Contribution to the Special Issue on Representation Theory and Integrable Systems in honor of Vitaly Tarasov on the 60th birthday and Alexander Varchenko on the 70th birthday

Perfect Integrability and Gaudin Models

Kang Lu
Department of Mathematics, University of Denver, 2390 S. York St., Denver, CO 80210, USA

Received August 26, 2020, in final form December 02, 2020; Published online December 10, 2020

We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite types, with periodic and regular quasi-periodic boundary conditions.

Key words: Gaudin model; Bethe ansatz; Frobenius algebra.

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