θ-Unitary representations for the W-algebra W(2,2)

Abstract

In this article, conjugate-linear anti-involutions and θ-unitary Harish-Chandra modules over the W-algebra W(2,2) are studied. It is proved that there are only two classes that conjugate-linear anti-involutions over W(2,2). The main result of this article is that a θ-unitary Harish-Chandra module over the W-algebra W(2,2) is simply a -unitary Harish-Chandra module over the Virasoro algebra and hence is either a simple highest or lowest weight module or a simple module from the intermediate series of the form A _a,b for some

Keywords:

• the W-algebra W(2,2)
• Harish-Chandra module
• θ-unitary module

AMS Subject Classifications::

• 17B10
• 17B40
• 17B68

Acknowledgements

This was supported by the National Natural Science Foundation of China (No. 10931006).