# Formulae of $\imath$-divided powers in ${\bf U}_q(\mathfrak{sl}_2)$, II

@article{Wang2018FormulaeO, title={Formulae of \$\imath\$-divided powers in \$\{\bf U\}_q(\mathfrak\{sl\}_2)\$, II}, author={Weiqiang Wang and Collin Berman}, journal={arXiv: Representation Theory}, year={2018} }

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 $\imath$-canonical basis (also known as the $\imath$-divided powers) for the coideal subalgebra of the quantum $\mathfrak{sl}_2$ were established by Bao and Wang. We establish closed formulae for the $\imath$-divided powers as polynomials in $t$ and also in terms of Chevalley generators of the quantum $\mathfrak{sl}_2$ when the parameterâ€¦Â Expand

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