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Braid Group Action and Quantum Affine Algebras

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arxiv hep-th/9404165 v1 pith:46BGWWQW submitted 1994-04-27 hep-th math.QA

Jonathan Beck This is my paper · ORCID
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keywords actionaffinegroupalgebrabraidquantumalgebrasbasis
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abstract

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy the relations of Drinfel$'$d's new realization. Coproduct formulas are given and a PBW type basis is constructed.

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  1. Using the quantum torus to investigate the $q$-Onsager algebra

    math.QA 2025-04 conditional novelty 6.0 of 10

    The Baseilhac-Kolb and Lu-Wang root-vector elements of the q-Onsager algebra are expressed as explicit Laurent monomials in the quantum torus.

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