Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group

Abstract

We study the Rumin differentials of the 5-dimensional graded nilpotent Lie group that appears as osculating group of generic rank two distributions in dimension five. In irreducible unitary representations of this group, the Rumin differentials provide intriguing generalizations of the classical quantum harmonic oscillator. For the Schrodinger representations, we compute the spectrum and the zeta regularized determinant of each Rumin differential. In the generic representations, we evaluate their alternating product, i.e., the analytic torsion of the Rumin complex.

v2: minor changes in the introduction and Section 4; added Remark 2 (p.49), Remark 3 (p54), and Corollary 1 (p.55); fixed some typos; no substantial changes; now 64 pages

References in corpus (14)

• Differential equations and conformal structures
• The twistor spinors of generic 2- and 3-distributions
• Graded hypoellipticity of BGG sequences
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• The heat asymptotics on filtered manifolds
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• Analytic torsion of generic rank two distributions in dimension five
• On 5-manifolds admitting rank two distributions of Cartan type
• Analytic torsions associated with the Rumin complex on contact spheres
• From exact-WKB towards singular quantum perturbation theory
• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates
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• Analytic torsion of nilmanifolds with (2,3,5) distributions

Cited by in corpus (1)

• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates