Reflection matrices for quantum symmetric pairs of affine type

Vidas Regelskis; Bart Vlaar

Reflection matrices for quantum symmetric pairs of affine type

Mathematics

Research output: Working paper › Preprint

Abstract

We provide a classification of reflection matrices for the vector representation of quantum symmetric pairs described by untwisted affine Satake diagrams. The reflection matrices are found by solving the associated boundary intertwining equation. In most cases they have no more than two nonzero entries in each row and column. We demonstrate equivalence relations for reflection matrices which are connected to symmetry properties of the vector representation and Hopf algebra automorphisms of the affine quantum groups. We use this to show that each reflection matrix found in this way is equivalent to one with at most two free parameters. Additional characteristics of the reflection matrices such as eigenvalues and affinization relations are also obtained.

Original language	English
Publication status	Published - 26 Feb 2016

Bibliographical note

99 pages, 23 tables; v.2: results for non-quasistandard quantum symmetric pair algebras included, simplifications and minor notation changes throughout

Keywords

math-ph
math.MP
math.QA
math.RT
nlin.SI

Access to Document

https://arxiv.org/abs/1602.08471

Cite this

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abstract = "We provide a classification of reflection matrices for the vector representation of quantum symmetric pairs described by untwisted affine Satake diagrams. The reflection matrices are found by solving the associated boundary intertwining equation. In most cases they have no more than two nonzero entries in each row and column. We demonstrate equivalence relations for reflection matrices which are connected to symmetry properties of the vector representation and Hopf algebra automorphisms of the affine quantum groups. We use this to show that each reflection matrix found in this way is equivalent to one with at most two free parameters. Additional characteristics of the reflection matrices such as eigenvalues and affinization relations are also obtained.",

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N2 - We provide a classification of reflection matrices for the vector representation of quantum symmetric pairs described by untwisted affine Satake diagrams. The reflection matrices are found by solving the associated boundary intertwining equation. In most cases they have no more than two nonzero entries in each row and column. We demonstrate equivalence relations for reflection matrices which are connected to symmetry properties of the vector representation and Hopf algebra automorphisms of the affine quantum groups. We use this to show that each reflection matrix found in this way is equivalent to one with at most two free parameters. Additional characteristics of the reflection matrices such as eigenvalues and affinization relations are also obtained.

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