Regularity of some invariant distributions on nice symmetric pairs
Representation Theory
2014-07-08 v2
Abstract
J.~Sekiguchi determined the semisimple symmetric pairs (g,h), called nice symmetric pairs, on which there is no non-zero invariant eigendistribution with singular support. On such pairs, we study regularity of invariant distributions annihilated by a polynomial of the Casimir operator. We deduce that invariant eigendistributions on (gl(4,R),gl(2,R)*gl(2,R)) are locally integrable functions.
Keywords
Cite
@article{arxiv.1407.0934,
title = {Regularity of some invariant distributions on nice symmetric pairs},
author = {Pascale Harinck},
journal= {arXiv preprint arXiv:1407.0934},
year = {2014}
}
Comments
E. Galina and Y. Laurent obtained stronger results on invariant distributions on nice symmetric pairs by different methods based on algebraic properties of D-modules (see references)