Serre-Lusztig relations for $ı$quantum groups

Abstract

Let $(\mathbf{U},{\mathbf{U}}^{ı})$ be a quantum symmetric pair of Kac-Moody type. The $ı$quantum groups ${\mathbf{U}}^{ı}$ and the universal $ı$quantum groups ${\tilde{\mathbf{U}}}^{ı}$ can be viewed as a generalization of quantum groups and Drinfeld doubles $\tilde{\mathbf{U}}$. In this paper we formulate and establish Serre-Lusztig relations for $ı$quantum groups in terms of $ı$divided powers, which are an $ı$-analog of Lusztig's higher order Serre relations for quantum groups. This has applications to braid group symmetries on $ı$quantum groups.

v3, 42 pages, mild corrections, to appear in CMP

References in corpus (1)

• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model

Cited by in corpus (5)

• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• Relative braid group symmetries on $ı$quantum groups of Kac-Moody type
• Tensor K-matrices for quantum symmetric pairs
• Serre-Lusztig relations for $ı$quantum groups II
• Quantum Howe duality and Schur duality of type AIII