Infinite-dimensional representations of $U_q(\mathfrak{sl}_2)$ and the shadow world: quantum $6j$-symbols for Verma modules
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| 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 |