The trigonometric spin Ruijsenaars-Schneider model is quantized from K-theoretic Coulomb branch data, with commuting Hamiltonians and quantum spin commutation relations derived.
The trigonometric counterpart of the Haldane Shastry Model
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abstract
The hierarchy of Integrable Spin Chain Hamiltonians, which are trigonometric analogs of the Haldane Shastry Model and of the associated higher conserved charges, is derived by a reduction from the trigonometric Dynamical Models of Bernard-Gaudin-Haldane-Pasquier. The Spin Chain Hamiltonians have the property of $U_q(\hat{gl}_2)$-invariance. The spectrum of the Hamiltonians and the $U_q(\hat{gl}_2)$-representation content of their eigenspaces are found by a descent from the Dynamical Models.
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Quantum Trigonometric Spin Ruijsenaars-Schneider Models from $K$-theoretic Coulomb Branches
The trigonometric spin Ruijsenaars-Schneider model is quantized from K-theoretic Coulomb branch data, with commuting Hamiltonians and quantum spin commutation relations derived.