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arXiv · 2312.13256

Extended Baxter relations and QQ-systems for quantum affine algebras

Edward Frenkel·David Hernandez
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Abstract

Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works arXiv:1308.3444 and arXiv:1606.05301. In the present paper, we conjecture a family of analogous relations labeled by elements of the Weyl group W of g, so that the original relations correspond to the identity element. These relations are closely connected to the W-symmetry of q-characters established in arXiv:2211.09779. We prove these relations for all w in W if g has rank two, and we prove the extended TQ-relations if w is a simple reflection. We also generalize our results and conjectures to the shifted quantum affine algebras.

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Edward Frenkel, David Hernandez. 2024-05-29. Extended Baxter relations and QQ-systems for quantum affine algebras. https://arxiv.org/abs/2312.13256

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