Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

Pascal Baseilhac; Zengo Tsuboi

doi:10.1016/j.nuclphysb.2018.02.017

Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

Mathematical Physics 2018-03-12 v2 High Energy Physics - Theory math.MP Quantum Algebra

Authors: Pascal Baseilhac , Zengo Tsuboi

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Abstract

We consider intertwining relations of the augmented $q$ -Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary $K$ -operators in terms of the Cartan element of $U_{q}(sl_2)$ . These $K$ -operators solve reflection equations. Taking appropriate limits of these $K$ -operators in Verma modules, we derive $K$ -operators for Baxter Q-operators and corresponding reflection equations.

Keywords

augmented q-onsager algebra boundary k-operators baxter q-operators reflection equations verma modules intertwining relations cartan element

Cite

@article{arxiv.1707.04574,
  title  = {Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators},
  author = {Pascal Baseilhac and Zengo Tsuboi},
  journal= {arXiv preprint arXiv:1707.04574},
  year   = {2018}
}

Comments

45 pages, v2: universal T- and Q-operators added

Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

Abstract

Keywords

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