Formulae of $ı$-divided powers in ${\mathbf{U}}_q({\mathfrak{sl}}_2)$, II

Abstract

The coideal subalgebra of the quantum ${\mathfrak{sl}}_2$ is a polynomial algebra in a generator $t$ which depends on a parameter $\kappa$. The existence of the $ı$-canonical basis (also known as the $ı$-divided powers) for the coideal subalgebra of the quantum ${\mathfrak{sl}}_2$ were established by Bao and Wang. We establish closed formulae for the $ı$-divided powers as polynomials in $t$ and also in terms of Chevalley generators of the quantum ${\mathfrak{sl}}_2$ when the parameter $\kappa$ is an arbitrary $q$-integer. The formulae were known earlier when $\kappa =0,1$.

v2, updated references, final version

References in corpus (3)

• Formulae of $ı$-divided powers in ${\mathbf{U}}_q({\mathfrak{sl}}_2)$
• Canonical bases arising from quantum symmetric pairs
• Multiparameter quantum Schur duality of type B

Cited by in corpus (3)

• Canonical bases arising from quantum symmetric pairs of Kac-Moody type
• Crystal bases of modified $ı$quantum groups of certain quasi-split types
• Canonical bases arising from $ı$quantum covering groups