The category of quasi-Whittaker modules over the Schrödinger algebra

Abstract

Simple quasi-Whittaker modules over the Schrödinger algebra $s_1$ of $(1+1)$-dimensional space-time were originally introduced and classified by Cai, Cheng, Shen in their work [7]. In the present paper, our focus lies in the study of the category of quasi-Whittaker modules over $s_1$. We show that each non-singular block is equivalent to the category of finite-dimensional modules over the polynomial algebra in one variable. In particular, we can give explicit realizations of simple quasi-Whittaker modules using differential operators.