2024/06/17 by Catharina Stroppel, Stroppel, Catharina, Zbigniew Wojciechowski +1
Computer Science · #16T30 #17B37 #20C08 #22E46 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.12132
openalex publication_date 2024/06/17 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28
We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum \mathfraksl2 to a coideal subalgebra. We realise the category as module category over the monoidal category of type ±1 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.