Diagrammatics for the smallest quantum coideal and Jones--Wenzl projectors
Abstract
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 $\Theta$-networks.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.12132
- arXiv:
- arXiv:2406.12132
- Bibcode:
- 2024arXiv240612132S
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Combinatorics;
- Mathematics - Quantum Algebra;
- 17B37;
- 22E46;
- 16T30;
- 20C08
- E-Print:
- This is partially based on the second authors Master Thesis from 2022