Quantum affine algebras and spectral k-matrices

Andrea Appel (University of Parma, Italy)

22-Mar-2021, 15:00-16:00 (3 years ago)

Abstract: The Yang-Baxter equation (YBE) and the reflection equation (RE) are two fundamental symmetries in mathematics arising from particles moving along a line or a half-line. The quest for constant solutions of YBE (R-matrices) is at the very origin of the Drinfeld-Jimbo quantum groups and their universal R-matrix. Similarly, constant solutions of RE (k-matrices) naturally appear in the context of quantum symmetric pairs (QSP).

In joint work with Bart Vlaar, we construct a discrete family of universal k-matrices associated to an arbitrary quantum symmetric Kac-Moody pair as operators on category O integrable representations. This generalises previous results by Balagovic-Kolb and Bao-Wang valid for finite-type QSP. In this talk, I will explain how, in affine type, this construction gives rise to parameter-dependent operators (spectral k-matrices) on finite-dimensional representations of quantum loop algebras solving the same RE introduced by Cherednik and Sklyanin in the 1980s in the context of quantum integrability near a boundary.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic


Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

Organizers: Rubén Martos, Frank Taipe*, Makoto Yamashita
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