# Chris Chung

## Papers

- Canonical bases arising from ıquantum covering groups

arXiv version## Abstract: (click to expand)

For ıquantum covering groups (U,U

^{ı}) of super Kac-Moody type, we construct ı-canonical bases for the highest weight integrable U-modules and their tensor products regarded as U^{ı}-modules, as well as a canonical basis for the modified form of the ıquantum covering group U^{ı}, using the ı^{π}-divided powers, rank one canonical basis for U^{ı}. - A Serre Presentation for the ıQuantum Covering Groups

arXiv version## Abstract: (click to expand)

Let (U,U

^{ı}) be a quasi-split quantum symmetric pair of Kac-Moody type. The ıquantum group 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 U_{π}^{ı}of quantum symmetric pairs (U_{π},U_{π}^{ı}) for quantum covering algebras U_{π}, which have an additional parameter π that specializes to the Lusztig quantum group when π=1 and quantum supergroups of anisotropic type when π=−1. We give a Serre presentation for U_{π}^{ı}, introducing the ı^{π}-Serre relations and ı^{π}-divided powers. - Quantum Supergroups VI: Roots of 1 (with Thomas Sale and Weiqiang Wang)

*Lett. Math. Phys.***109**(2019), pp. 2753–2777

arXiv version journal version## Abstract: (click to expand)

A quantum covering group is an algebra with parameters q and π subject to π²=1, and it admits an integral form; it specializes to the usual quantum group at π=1 and to a quantum supergroup of anisotropic type at π=−1. In this paper we establish the Frobenius–Lusztig homomorphism and Lusztig–Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at π=1 recovers Lusztig’s constructions for quantum groups at roots of 1.