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Corpus ID: 119117589

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

@article{Berman2017FormulaeO,
title={Formulae of \$\imath\$-divided powers in \$\{\mathbf U\}_q(\mathfrak\{sl\}_2)\$},
author={Collin Berman and W. Wang},
journal={arXiv: Representation Theory},
year={2017}
}

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, with conjectural explicit formulae. In this paper we prove the conjectured formulae of these $\imath$-divided powers. This is achieved by first establishing closed formulae of the $\imath$-divided powers in basis for quantum $\mathfrak{sl}_2$ and then formulae for the $\imath$-canonical basis in terms of Lusztig's… Expand