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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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