Infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ and the shadow world: quantum $6j$-symbols for Verma modules

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autor principal: Solovyev, Dmitry
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866908573945036800
author Solovyev, Dmitry
author_facet Solovyev, Dmitry
contents This paper initiates the study of invariants of links associated to infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ using graphical representation for quantum $6j$-symbols, the shadow world. We obtain formulae for $q3j$-symbols and $q6j$-symbols for Verma modules and study their properties. This hints at the structure of the possible target category for Reshetikhin-Turaev functor for such an invariant.
format Preprint
id arxiv_https___arxiv_org_abs_2410_18463
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ and the shadow world: quantum $6j$-symbols for Verma modules
Solovyev, Dmitry
Representation Theory
Quantum Algebra
This paper initiates the study of invariants of links associated to infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ using graphical representation for quantum $6j$-symbols, the shadow world. We obtain formulae for $q3j$-symbols and $q6j$-symbols for Verma modules and study their properties. This hints at the structure of the possible target category for Reshetikhin-Turaev functor for such an invariant.
title Infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ and the shadow world: quantum $6j$-symbols for Verma modules
topic Representation Theory
Quantum Algebra
url https://arxiv.org/abs/2410.18463