The local character expansion as branching rules: nilpotent cones and the case of SL(2)\mathrm{SL}(2)

We show there exist representations of each maximal compact subgroup $K$ of the $p$-adic group $G=\mathrm{SL}(2,F)$, attached to each nilpotent coadjoint orbit, such that every irreducible representation of $G$, upon restriction to a suitable subgroup of $K$, is a sum of these five representations in the Grothendieck group. This is a representation-theoretic analogue of the analytic local character expansion due to Harish-Chandra and Howe. Moreover, we show for general connected reductive groups that the wave front set of many irreducible positive-depth representations of $G$ are completely determined by the nilpotent support of their unrefined minimal $K$-types.Comment: 32 pages; added references to recent related work of Henniart-Vign\'era

Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliographical references (p. 52-53).by Monica Nevins.Ph.D

Branching Rules for Supercuspidal Representations of SL_2(k)

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this decomposition in the case that the residual characteristic is odd, and determine how the spectrum of this decomposition varies as a function of the parameters describing the supercuspidal representation.Comment: 30 pages; minor reorganization to previous version. Accepted to Journal of Algebr

Patient and public involvement in pragmatic trials : online survey of corresponding authors of published trials

Acknowledgements The authors acknowledge Dr. Paxton Montgomery Moon, Alison Howie, Hayden Nix and Dr. Merrick Zwarenstein for their contributions to the data extraction. They also thank Drs. Bruno Giraudeau and Agnes Caille (University of Tours), Dr. Laura Hanson (University of North Carolina School of Medicine) and Dr. Jill Harrison (Brown University) for assistance with pilot testing of the survey questionnaire. Funding: This work was supported by the Canadian Institutes of Health Research through the Project Grant competition (competitive, peer-reviewed), award number PJT-153045, and the National Institute of Aging ( NIA) of the National Institutes of Health under Award Number U54AG063546, which funds NIA Imbedded Pragmatic Alzheimer’s Disease and Related Dementias Clinical Trials Collaboratory ( NIA IMPACT Collaboratory). The funders had no role in the study design; in the collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.Peer reviewedPublisher PD