Transfer operators and Hankel transforms: horospherical limits and quantization
Abstract
Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties of rank one, and gave an interpretation of them in terms of geometric quantization. In this paper, I study how these operators vary in the horospherical limits of these varieties, where they have a conceptual interpretation related to scattering theory. I also revisit Jacquet's Hankel transform for the Kuznetsov formula, which is related to the functional equation of the standard L-function of GL(n), and provide an interpretation of it in terms of quantization.
Keywords
Cite
@article{arxiv.2407.19500,
title = {Transfer operators and Hankel transforms: horospherical limits and quantization},
author = {Yiannis Sakellaridis},
journal= {arXiv preprint arXiv:2407.19500},
year = {2024}
}
Comments
57pp. To appear in "Symmetry in Geometry and Analysis---Festschrift for Toshiyuki Kobayashi."