Certain Induced Complementary Series of the Universal Covering of the Symplectic Group

TL;DR

This paper constructs specific induced complementary series representations for the universal covering of symplectic groups, expanding the known classes of such representations beyond linear groups using invariant tensor products.

Contribution

It introduces a new method to build these representations via invariant tensor products applied to degenerate series on the Shilov boundary.

Findings

Constructed new induced complementary series for the universal covering of symplectic groups.

Extended the class of known representations beyond linear groups.

Demonstrated the application of invariant tensor products in this context.

Abstract

In this paper, we give a construction of certain induced complementary series of the universal covering of the symplectic groups. There are abundant such representations besides those of linear groups. We achieve this by applying invariant tensor product to degenerate complementary series on the Shilov boundary.