Whittaker modules for the Schrödinger–Witt algebra

Abstract

In this paper, Whittaker modules for the Schrödinger-Witt algebra sv are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. sv has a triangular decomposition according to its Cartan subalgebra h: sv = sv − h sv + . For any Lie algebra homomorphism : sv + → C, we can define Whittaker modules of type . When is nonsingular, the Whittaker vectors, the irreducibility, and the classification of Whittaker modules are completely determined. When is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special .

Whittaker modules for a Lie algebra of Block type

“…In the quantum setting, Whittaker modules have been studied by Sevoystanov for U h (g) [8] and by Ondrus for U q (sl 2 ) [6]. Recently, Whittaker modules have also been studied by Ondrus and Wiesner for the Virasoro algebra [7], Zhang and Tan for Schrödinger-Virasoro algebra [17], Christodoulopoulou for Heisenberg algebras [2], and by Benkart and Ondrus for generalized Weyl algebras [1].…”

Simple Schrödinger modules which are locally finite over the positive part

“…(see Refs. [14][15][16][17][18][19][20][21][22][23]). Moreover, quantum deformation of Whittaker modules and modules induced from Whittaker modules are also studied (see Refs.…”

Quasi-Whittaker modules over the conformal Galilei algebras

“…Then the idea was exploited and generalized to consider modules over infinite-dimensional Lie algebras (e.g. [8][9][10][11][12][13][14]). The traditional definition of Whittaker modules is closely tied to the triangular decomposition of a Lie algebra.…”