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ON THE REGULARITY OF D-MODULES GENERATED BY RELATIVE CHARACTERS

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Abstract

Following the ideas of Ginzburg, for a subgroup K of a connected reductive ℝ-group G we introduce the notion of K-admissible D-modules on a homogeneous G-variety Z. We show that K-admissible D-modules are regular holonomic when K and Z are absolutely spherical. This framework includes: (i) the relative characters attached to two spherical subgroups H1 and H2, provided that the twisting character χi factors through the maximal reductive quotient of Hi, for i = 1; 2; (ii) localization on Z of Harish-Chandra modules; (iii) the generalized matrix coeficients when K(ℝ) is maximal compact. This complements the holonomicity proven by Aizenbud–Gourevitch–Minchenko. The use of regularity is illustrated by a crude estimate on the growth of K-admissible distributions based on tools from subanalytic geometry.

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  1. Beijing International Center for Mathematical Research/School of Mathematical Sciences, Peking University, No. 5 Yiheyuan Road, Beijing, 100871, People’s Republic of China

    WEN-WEI LI

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WEN-WEI LI is supported by NSFC-11922101.

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LI, WW. ON THE REGULARITY OF D-MODULES GENERATED BY RELATIVE CHARACTERS. Transformation Groups 27, 525–562 (2022). https://doi.org/10.1007/s00031-020-09624-x

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