Mukhin, EugeneYoung, C. A. S.2016-03-312016-03-312014-05Mukhin, E., & Young, C. (2014). Affinization of category 𝒪 for quantum groups. Transactions of the American Mathematical Society, 366(9), 4815-4847.https://hdl.handle.net/1805/9117Let be a simple Lie algebra. We consider the category of those modules over the affine quantum group whose -weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category . In particular, we define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.enIUPUI Open Access Policyminimal affinizationsWeyl denominator type formulaArticle