Non-decreasable K-types are unitarily small

Abstract

Let $G$ be a connected simple non-compact real reductive Lie group with a maximal compact subgroup $K$. This note aims to show that any non-decreasable $K$-type (in the sense of the first named author) is unitarily small (in the sense of Salamanca-Riba and Vogan). This answers Conjecture 2.1 of \cite{D} in the affirmative.