Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras

TL;DR

This paper establishes the existence and uniqueness of crystal bases for parabolic Verma modules over quantum orthosymplectic superalgebras, linking them to polynomial representations of general linear Lie superalgebras.

Contribution

It introduces a novel construction of crystal bases for these modules, extending the theory of quantum superalgebra representations.

Findings

Existence of a unique crystal base for the modules

Connection to polynomial representations of Lie superalgebras

Extension of crystal base theory to superalgebra context

Abstract

We show that there exists a unique crystal base of a parabolic Verma module over a quantum orthosymplectic superalgebra, which is induced from a $q$-analogue of a polynomial representation of a general linear Lie superalgebra.