A Serre presentation for the $ı$quantum groups

Abstract

Let $(\mathbf{U},{\mathbf{U}}^{ı})$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node. We give a presentation of the $ı$quantum group ${\mathbf{U}}^{ı}$ with explicit $ı$Serre relations. The verification of new $ı$Serre relations is reduced to some new q-binomial identities. Consequently, ${\mathbf{U}}^{ı}$ is shown to admit a bar involution under suitable conditions on the parameters.

v4, sign in (3.8) corrected, reference updated, final version for Transform. Groups

References in corpus (4)

• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• Canonical bases arising from quantum symmetric pairs of Kac-Moody type
• Formulae of $ı$-divided powers in ${\mathbf{U}}_q({\mathfrak{sl}}_2)$
• Generalized Onsager algebras

Cited by in corpus (9)

• Canonical bases arising from quantum symmetric pairs of Kac-Moody type
• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• Lectures on dualities ABC in representation theory
• Defining relations for quantum symmetric pair coideals of Kac-Moody type
• Braid group symmetries on quasi-split $ı$quantum groups via $ı$Hall algebras
• Serre-Lusztig relations for $ı$quantum groups III
• Crystal bases of modified $ı$quantum groups of certain quasi-split types
• A Serre presentation for the $ı$quantum covering groups
• Canonical bases arising from $ı$quantum covering groups