# Baxter Operator and Baxter Equation for $q$-Toda and Toda$_2$ Chains

Abstract : We construct the Baxter operator Q(λ) for the q-Toda chain and the Toda2 chain (the Toda chain in the second Hamiltonian structure). Our construction builds on the relation between the Baxter operator and Bäcklund transformations that were unravelled in [13]. We construct a number of quantum intertwiners ensuring the commutativity of Q(λ) with the transfer matrix of the models and of the Q’s between each other. Most importantly, Q(λ) is modular invariant in the sense of Faddeev. We derive the Baxter equation for the eigenvalues q(λ) of Q(λ) and show that these are entire functions of λ. This last property will ultimately lead to the quantization of the spectrum for the considered Toda chains, in a subsequent publication [1]. This work is dedicated to the memory of L. D. Faddeev
Type de document :
Article dans une revue
Rev.Math.Phys., 2018, 30 (06), pp.1840003. 〈10.1142/S0129055X18400032〉

https://hal.archives-ouvertes.fr/hal-01846841
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Soumis le : dimanche 22 juillet 2018 - 22:11:39
Dernière modification le : samedi 23 mars 2019 - 01:39:47

### Citation

Olivier Babelon, Karol K. Kozlowski, Vincent Pasquier. Baxter Operator and Baxter Equation for $q$-Toda and Toda$_2$ Chains. Rev.Math.Phys., 2018, 30 (06), pp.1840003. 〈10.1142/S0129055X18400032〉. 〈hal-01846841〉

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