A geometric setting for quantum osp(1|2)

TL;DR

This paper provides a geometric categorification framework for large finite-dimensional quotients of quantum osp(1|2) and explores their relation to quantum sl(2), revealing isomorphisms over specific fields.

Contribution

It introduces a new geometric categorification for quantum osp(1|2) quotients and establishes their isomorphism with modified quantum sl(2).

Findings

Categorification of quantum osp(1|2) quotients.

Isomorphism between modified quantum osp(1|2) and quantum sl(2).

New version of modified quantum osp(1|2) introduced.

Abstract

A geometric categorification is given for arbitrary-large-finite-dimensional quotients of quantum osp(1|2) and the tensor product of its simple modules. The modified quantum osp(1|2) of Clark-Wang, a new version in this paper and the modified quantum sl(2) are isomorphic to each other over a field containing Q(v) and a root of -1.