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  Universal K-matrices for quantum Kac-Moody algebras

Appel, A., & Vlaar, B. (2022). Universal K-matrices for quantum Kac-Moody algebras. Representation Theory, 26, 764-824. doi:10.1090/ert/623.

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Appel-Vlaar_Universal K-matrices for quantum Kac-Moody algebras_2022.pdf (Publisher version), 729KB
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 Creators:
Appel, Andrea, Author
Vlaar, Bart1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Representation Theory, Mathematical Physics, Quantum Algebra
 Abstract: We introduce the notion of a cylindrical bialgebra, which is a
quasitriangular bialgebra H endowed with a universal K-matrix, i.e., a
universal solution of a generalized reflection equation, yielding an action of
cylindrical braid groups on tensor products of its representations. We prove
that new examples of such universal K-matrices arise from quantum symmetric
pairs of Kac-Moody type and depend upon the choice of a pair of generalized
Satake diagrams. In finite type, this yields a refinement of a result obtained
by Balagovi\'c and Kolb, producing a family of non-equivalent solutions
interpolating between the quasi-K-matrix and the full universal K-matrix.
Finally, we prove that this construction yields formal solutions of the
generalized reflection equation with a spectral parameter in the case of
finite-dimensional representations over the quantum affine algebra
$U_qL\mathfrak{sl}_2$.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2007.09218
DOI: 10.1090/ert/623
 Degree: -

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Title: Representation Theory
  Abbreviation : ERT
Source Genre: Journal
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Publ. Info: American Mathematical Society
Pages: - Volume / Issue: 26 Sequence Number: - Start / End Page: 764 - 824 Identifier: -