Relative braid group symmetries on $ı$quantum groups of Kac-Moody type

Abstract

Recently, relative braid group actions on $ı$quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction to $ı$quantum groups of Kac-Moody type. We formulate root vectors for $ı$quantum groups in both recursive forms and closed $ı$divided power forms. We show that the relative braid group symmetries send root vectors to root vectors.

arXiv commentv3, corrected formulas (3.17)-(3.18); 46 pages

References in corpus (7)

• Quantum symmetric Kac-Moody pairs
• The half-infinite XXZ chain in Onsager's approach
• Hall algebras and quantum symmetric pairs II: reflection functors
• Hall algebras and quantum symmetric pairs of Kac-Moody type
• Universal K-matrices for quantum Kac-Moody algebras
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Cited by in corpus (1)

• Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs