Inductive algebras and homogeneous shifts

TL;DR

This paper classifies inductive algebras for certain group representations and derives a new classification of homogeneous shift operators, offering a novel perspective on previous results by Bagchi and Misra.

Contribution

It provides a new classification of homogeneous shift operators via inductive algebras for specific group representations, advancing the theoretical understanding.

Findings

Classification of inductive algebras for the universal cover of SL(2,R)

New approach to homogeneous shift operators

Connections to prior work by Bagchi and Misra

Abstract

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This gives a new approach to the results of Bagchi and Misra.