On the dimension datum of a subgroup. II

TL;DR

This paper explores advanced aspects of dimension data in Lie groups, including a generalized tau-dimension datum, the behavior of disconnected subgroups, and the compactness properties of isospectral spaces.

Contribution

Introduces the tau-dimension datum, extends dimension data analysis to disconnected subgroups, and investigates the compactness of isospectral sets in homogeneous spaces.

Findings

Defined the tau-dimension datum as a generalization.

Analyzed dimension data for disconnected subgroups.

Proved compactness of isospectral sets of normal homogeneous spaces.

Abstract

This paper studies three aspects around dimension datum: (1), a generalization of the dimension datum, which we call the tau-dimension datum; (2), dimension data of disconnected subgroups; (3), compactness of isospectral sets of normal homogeneous spaces.