A Serre presentation for the $ı$quantum covering groups

Abstract

Let $(\mathbf{U},{\mathbf{U}}^{ı})$ be a quasi-split quantum symmetric pair of Kac-Moody type. The $ı$quantum group ${\mathbf{U}}^{ı}$ admits a Serre presentation featuring the $ı$-Serre relations in terms of $ı$-divided powers. Generalizing this result, we give a Serre presentation ${\mathbf{U}}_{\pi }^{ı}$ of quantum symmetric pairs $({\mathbf{U}}_{\pi },{\mathbf{U}}_{\pi }^{ı})$ for quantum covering algebras ${\mathbf{U}}_{\pi }$, which have an additional parameter $\pi$ that specializes to the Lusztig quantum group when $\pi =1$ and quantum supergroups of anisotropic type when $\pi =-1$. We give a Serre presentation for ${\mathbf{U}}_{\pi }^{ı}$, introducing the ${ı}^{\pi }$-Serre relations and ${ı}^{\pi }$-divided powers.

28 pages including references. arXiv admin note: text overlap with arXiv:1810.12475 by other authors

References in corpus (1)

• Quantum symmetric pairs at roots of $1$

Cited by in corpus (1)

• Canonical bases arising from $ı$quantum covering groups