Representation theory of the Reflection Equation Algebra II: Theory of shapes

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: De Commer, Kenny, Moore, Stephen T.
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866913416449359872
author De Commer, Kenny
Moore, Stephen T.
author_facet De Commer, Kenny
Moore, Stephen T.
contents We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We consider the Poisson structure appearing as the classical limit of the $R$-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape.
format Preprint
id arxiv_https___arxiv_org_abs_2407_03613
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Representation theory of the Reflection Equation Algebra II: Theory of shapes
De Commer, Kenny
Moore, Stephen T.
Quantum Algebra
Representation Theory
We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We consider the Poisson structure appearing as the classical limit of the $R$-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape.
title Representation theory of the Reflection Equation Algebra II: Theory of shapes
topic Quantum Algebra
Representation Theory
url https://arxiv.org/abs/2407.03613