The Wave Front Set Correspondence for Dual Pairs with One Member Compact

作     者：Mark MCKEE Angela PASQUALE Tomasz PRZEBINDA Mark MCKEE;Angela PASQUALE;Tomasz PRZEBINDA

作者机构：Hammond LaneProvidenceUT 84332USA Universite de LorraineCNRSIECLF-57000 MetzFrance Department of MathematicsUniversity of OklahomaNormanOK 73019USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第3期

页      面：823-869页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the University of Oklahoma for hospitality and financial support hospitality and financial support from the Université de Lorraine partial support from NSA (Grant No. H98230-13-1-0205) NSF (Grant No. DMS-2225892) 

主　　题：Reductive dual pairs Howe duality Weil representation wave front set orbital integrals 

摘      要：Let W be a real symplectic space and(G,G )an irreducible dual pair in Sp(W),in the sense of Howe,with G *** G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation II of G that occurs in the restriction of the Weil representation to G,let On denote its *** prove that,for a suitable embedding T of Sp(W)in the space of tempered distributions on W,the distribution T(On)admits an asymptotic limit,and the limit is a nilpotent orbital *** an application,we compute the wave front set of II ,the representation of G dual to II,by elementary means.