Whittaker modules for the Schrödinger-Virasoro algebra

Details Whittaker modules for the Schrödinger-Virasoro algebra Whittaker modules for the Schrödinger-Virasoro algebra

2008-12-17

arxiv.org/abs/0812.3245v6

Mathematics

Rings and Algebras

22 pages

Scientific paper

In this paper, Whittaker modules for the Schr\"odinger-Virasoro algebra $\mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $\mathfrak{sv}$ has a triangular decomposition according to the Cartan algebra $\mathfrak{h}:$ $$\mathfrak{sv}=\mathfrak{sv}^{-}\oplus\mathfrak{h}\oplus\mathfrak{sv}^{+}.$$ For any Lie algebra homomorphism $\psi:\mathfrak{sv}^{+}\to\mathbb{C}$, we can define Whittaker modules of type $\psi.$ When $\psi$ is nonsingular, the Whittaker vectors, the irreducibility and the classification of Whittaker modules are completely determined. When $\psi$ 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 $\psi$.

Affiliated with

Also associated with

No associations

Rating

Whittaker modules for the Schrödinger-Virasoro algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Whittaker modules for the Schrödinger-Virasoro algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Whittaker modules for the Schrödinger-Virasoro algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-94776