Operator Product on Locally Symmetric Spaces of Rank One and the Multiplicative Anomaly

TL;DR

This paper investigates the multiplicative anomaly of Laplace type operators on rank one symmetric spaces, deriving explicit formulas and exact values for various classes and dimensions, enhancing understanding of their global multiplicative properties.

Contribution

It provides the first explicit formulas and exact calculations of the multiplicative anomaly for Laplace operators on irreducible rank one symmetric spaces.

Findings

Explicit form of the multiplicative anomaly derived

Exact values calculated for key classes of spaces

Enhanced understanding of global multiplicative properties

Abstract

The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for important classes of locally symmetric spaces and different dimensions.