Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9445
Title: On infinitesimal τ -isospectrality of locally symmetric spaces
Authors: BHAGWAT, CHANDRASHEEL
MONDAL, KAUSTABH
Sachdeva, Gunja
Dept. of Mathematics
Keywords: Representation equivalence
Isospectrality
Selberg trace formula
Non-compact symmetric space
2025-MAR-WEEK1
2025
TOC-MAR-2025
Issue Date: Jan-2025
Publisher: Cambridge University Press
Citation: Canadian Mathematical Bulletin, 68(01), 246 – 261.
Abstract: Let (τ,Vτ) be a finite dimensional representation of a maximal compact subgroup K of a connected non-compact semisimple Lie group G, and let Γ be a uniform torsion-free lattice in G. We obtain an infinitesimal version of the celebrated Matsushima–Murakami formula, which relates the dimension of the space of automorphic forms associated to τ and multiplicities of irreducible τ∨ -spherical spectra in L2(Γ∖G) . This result gives a promising tool to study the joint spectra of all central operators on the homogenous bundle associated to the locally symmetric space and hence its infinitesimal τ -isospectrality. Along with this, we prove that the almost equality of τ -spherical spectra of two lattices assures the equality of their τ -spherical spectra.
URI: https://doi.org/10.4153/S0008439524000882
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9445
ISSN: 0008-4395
1496-4287
Appears in Collections:JOURNAL ARTICLES

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