The bar involution for quantum symmetric pairs -- hidden in plain sight

2021/04/13 by Stefan Kolb, Kolb, Stefan
Mathematics · #16T05 #17B67 #FOS: Mathematics #Primary: 17B37 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary: 53C35 #math.QA #math.RT #msc:16T05 #msc:17B37 #msc:17B67 #msc:53C35

paper · pdf · doi:10.48550/arxiv.2104.06120

9 pages

arxiv created 2021/04/13 · arxiv updated 2021/04/14

Abstract

We show that all quantum symmetric pair coideal subalgebras B_c of Kac-Moody type have a bar involution for a suitable choice of parameters c. The proof relies on a generalized notion of quasi K-matrix. The proof does not involve an explicit presentation of B_c in terms of generators and relations.

Related

• Quantum symmetric Kac–Moody pairs
• Universal K-matrix for quantum symmetric pairs
• Coideal Subalgebras and Quantum Symmetric Pairs
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• A new involution for quantum loop algebras