Diagrammatics for the smallest quantum coideal and Jones--Wenzl projectors
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909225948545024 |
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| author | Stroppel, Catharina Wojciechowski, Zbigniew |
| author_facet | Stroppel, Catharina Wojciechowski, Zbigniew |
| contents | We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum $\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module category over the monoidal category of type $\pm1$ representations in terms of string diagrams and via generators and relations. The idempotents projecting onto the quantized eigenspaces are described as type $B/D$ analogues of Jones--Wenzl projectors. As an application we introduce and give recursive formulas for analogues of $Θ$-networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diagrammatics for the smallest quantum coideal and Jones--Wenzl projectors Stroppel, Catharina Wojciechowski, Zbigniew Representation Theory Combinatorics Quantum Algebra 17B37, 22E46, 16T30, 20C08, We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum $\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module category over the monoidal category of type $\pm1$ representations in terms of string diagrams and via generators and relations. The idempotents projecting onto the quantized eigenspaces are described as type $B/D$ analogues of Jones--Wenzl projectors. As an application we introduce and give recursive formulas for analogues of $Θ$-networks. |
| title | Diagrammatics for the smallest quantum coideal and Jones--Wenzl projectors |
| topic | Representation Theory Combinatorics Quantum Algebra 17B37, 22E46, 16T30, 20C08, |
| url | https://arxiv.org/abs/2406.12132 |