Localised analytic torsion and relative analytic torsion for non compact Lie groups of type I
Year: 2024
Type: article
Abstract: Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $ρ$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$ localised at the representation $ρ$. Next, let $Γ$ a discrete cocompact subgroup of $G$. We use the localised analytic torsion to define the relative analytic torsion of the pair $(G,Γ)$, and we prove that it coincides with the Lott $L^2$ analytic torsion of a covering space. We illustrate these constructions analysing in some details two examples: the abelian case, and the case $G=H$, the Heisenberg group.
Source: Journal of Functional Analysis
Authors: A. Della Vedova, M. Spreafico
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,670
OpenAlex ID: W4402573503