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We review the status of a program, outlined and motivated in the introduction, for the study of correspondences between spectral invariants of partially hyperbolic flows on locally symmetric spaces and their quantizations. Further, we briefly sketch an extension of the program to graphs and quotients of higher rank affine buildings. Finally, we formulate a number of concrete problems which may be viewed as possible further steps to be taken in order to complete the program.

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Quantum-Classical Correspondences for Locally Symmetric Spaces

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  • 发表日期：

    2025年

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  • Joachim Hilgert

摘要

We review the status of a program, outlined and motivated in the introduction, for the study of correspondences between spectral invariants of partially hyperbolic flows on locally symmetric spaces and their quantizations. Further, we briefly sketch an extension of the program to graphs and quotients of higher rank affine buildings. Finally, we formulate a number of concrete problems which may be viewed as possible further steps to be taken in order to complete the program.