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<p>We introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.</p>

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The zeta determinant of the reduced Lorentz group localized at a representation

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • M. Spreafico

摘要

We introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.