{"id":355,"date":"2019-05-30T15:40:41","date_gmt":"2019-05-30T15:40:41","guid":{"rendered":"http:\/\/sites.rutgers.edu\/diana-shelstad\/?page_id=355"},"modified":"2022-04-02T18:38:47","modified_gmt":"2022-04-02T18:38:47","slug":"my-research","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/diana-shelstad\/my-research\/","title":{"rendered":"MY RESEARCH"},"content":{"rendered":"
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CURRENT <\/strong>and <\/strong>RECENT <\/strong>
\n(publications, preprints, links, etc.)<\/strong><\/h2>\n

 <\/p>\n

On some early sources for the notion of transfer in Langlands Functoriality<\/strong><\/p>\n

Part I: An Overview with Examples<\/strong><\/p>\n

The Genesis of the Langlands Program<\/em><\/p>\n

London Mathematical Society Lecture Note Series 467, Cambridge, 2021,\u00a0 pp. 387 – 400.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

shelstadearlysourcestransferPART1<\/a><\/p>\n

PART 2<\/strong> is in preparation and will be submitted elsewhere.<\/p>\n

 <\/p>\n

On stable transfer for real groups. <\/strong><\/p>\n

has new title:<\/p>\n

Beyond Endoscopy: an approach to stable-stable transfer at
\nthe archimedean places.<\/strong><\/p>\n

\u201cThis paper comes in three parts. In Part A, we describe the precise formulation of our main theorem on the stable-stable transfer for the archimedean places within the theme of Beyond Endoscopy envisaged recently by Langlands [Langlands-2010]. To arrive at our formulation and include explicit formulas, we prove several preparatory results for a connected reductive linear algebraic group that is defined over the real field R<\/strong>. A base change result for C<\/strong>\/R<\/strong> is included.\u201d<\/p>\n

A preprint for Part A will be posted as soon as available.<\/p>\n

\u201cPart B is focused on proof of our main theorem, along with the explicit formulas described in Part A. The final Part C is concerned with first applications of the main theorem.\u201d<\/p>\n

 <\/p>\n

On elliptic factors in real endoscopic transfer II<\/strong>, in preparation.<\/p>\n

\u201cA central underlying theme in endoscopic transfer is Waldspurger\u2019s ellipticity principle. It concerns tempered representations of real groups, and was proved (indirectly) via spectral methods. We prefer to start with the dual geometric side, i.e., with orbital integrals. There also, ellipticity is important and our methods provide, quickly and easily, a characterization of ellipticity on the (tempered) spectral side in terms of Langlands parameters. Our main purpose in this paper is then to describe some new explicit formulas related to ellipticity. These formulas have consequences for the finer structure of packets of representations, and they extend our study started in the paper On elliptic factors in real endoscopic transfer I in the case of standard endoscopic transfer. The standard transfer is our present main interest because we rely on it as a preliminary, but crucial, step in another paper where we describe a stable-stable transfer for the local contribution at the archimedean places to Langlands\u2019 envisioned Beyond Endoscopy program for a connected reductive group defined over a number field.\u201d<\/p>\n

 <\/p>\n

\u00a0On the structure of endoscopic transfer factors.<\/strong><\/p>\n

\u00a0Representation Theory, Automorphic Forms, and Complex Geometry <\/em><\/p>\n

\u00a0<\/em>International Press, Somerville, MA, 2020, pp. 81 – 105.<\/p>\n

\u00a0 shelstadstructureendofactors<\/a>\u00a0\u00a0 arXiv<\/a><\/p>\n

 <\/p>\n

On elliptic factors in real endoscopic transfer I.<\/strong><\/p>\n

Progress in Math\u00a0312, Birkh\u00e4user\u00a0(2015),\u00a0 <\/em> pp. 455 \u2013 504.<\/p>\n

shelstadellipticfactorsONE<\/a>\u00a0\u00a0\u00a0\u00a0 arXiv<\/a><\/p>\n<\/div>\n

\n

 <\/p>\n

Slides for talks:<\/strong><\/p>\n

here<\/a>, Oct 2012: shelstad24slides<\/a><\/p>\n

here<\/a>, May 2013: shelstadtalkschmidconf<\/a><\/p>\n

here,<\/a> May 2014: pdf here<\/a> \u00a0 Slide15: normalize integrals with |D|1\/2<\/sup><\/p>\n

 <\/p>\n

On splitting invariants and sign conventions in endoscopic transfer.<\/strong><\/p>\n

With R. Kottwitz, 19 pp.<\/p>\n

KSsplittingsigns<\/a>\u00a0\u00a0\u00a0\u00a0 arXiv<\/a><\/p>\n

 <\/p>\n

On geometric transfer in real twisted endoscopy.<\/strong><\/p>\n

Annals of Math,\u00a0 Vol. 176\u00a0 (2012),\u00a0 pp.\u00a01919 \u2013 1985.\u00a0 here<\/a><\/p>\n

shelstadtwgeomMay2012<\/a><\/p>\n

 <\/p>\n

Some results on endoscopic transfer. <\/strong><\/p>\n

Notes for Banff 2011 workshop on L-packets, 18 pp.<\/p>\n

ShelstadNotesJune2011<\/a>\u00a0 See also shelstadabstract121511<\/a><\/p>\n

 <\/p>\n

A note on real endoscopic transfer and pseudo-coefficients.<\/strong><\/p>\n

Preprint, preliminary version,\u00a0 Nov 2010,\u00a0 6 pp.<\/p>\n

shelstadnotepseudocoeffs<\/a><\/p>\n

 <\/p>\n

Examples in endoscopy for real groups.<\/strong><\/p>\n

Notes for talks, Banff 2008 summer school and workshop on stable trace formula,<\/p>\n

Galois representations and Shimura varieties, 59 pp.<\/p>\n

shelstadbanff08notes<\/a><\/p>\n

 <\/p>\n

Tempered endoscopy for real groups III: inversion of transfer and L-packet structure.<\/b><\/p>\n

Representation Theory,\u00a0 Vol. 12\u00a0 (2008),\u00a0 pp. 369 \u2013 402.\u00a0 here<\/a><\/p>\n

shelstadtempend3<\/a>\u00a0 Remark added, p. 48<\/h6>\n

 <\/p>\n

Tempered endoscopy for real groups II: spectral transfer factors.<\/strong><\/p>\n

\u81ea\u5b88\u5f62\u5f0f\u4e0eLanglands\u7eb2\u9886 \u00a0 Automorphic forms and the Langlands Program <\/em><\/p>\n

Higher Education Press\/ International Press,\u00a0 2009\/ 2010,\u00a0 pp. 236 \u2013 276.<\/p>\n

shelstadtempend2<\/a><\/h6>\n

 <\/p>\n<\/div>\n<\/div>\n

Tempered endoscopy for real groups I: geometric transfer with canonical factors.<\/strong><\/p>\n

Contemporary Math,\u00a0 Vol. 472\u00a0 (2008),\u00a0 pp. 215 \u2013 246.<\/p>\n

shelstadtempend1<\/a><\/p>\n

\n
\n

 <\/p>\n

SOME OLDER <\/strong><\/h2>\n

 <\/p>\n

Foundations of Twisted Endoscopy<\/em><\/strong><\/p>\n

Ast\u00e9risque,\u00a0 Vol. 255, 1999.<\/p>\n

With R. Kottwitz.<\/p>\n

KottwitzShelstadFoundationsTwistedEndoscopy<\/a><\/p>\n

Errata (January 2012) in KSsplittingsigns<\/a><\/p>\n

 <\/p>\n

A formula for regular unipotent germs.<\/strong><\/p>\n

Ast\u00e9risque,\u00a0 Vol. 171 \u2013 172 (1989),\u00a0 pp. 275 \u2013 277.<\/p>\n

shelstadformularegularunipotentgerms<\/a><\/p>\n

 <\/p>\n

Transfer and descent: some recent results. <\/strong><\/p>\n

Harmonic Analysis on Reductive Groups<\/em>, Birkh\u00e4user (1991),\u00a0 pp. 297 \u2013 304.<\/p>\n

shelstadtransferdescentresults<\/a><\/p>\n

 <\/p>\n

Base change and a matching theorem for real groups. <\/strong><\/p>\n

Noncommutative Harmonic Analysis and Lie Groups, <\/em>SLN 880 (1981),\u00a0 pp. 425 \u2013 482.<\/p>\n

shelstadrealbasechangefirstattempt<\/a><\/p>\n

 <\/p>\n

Endoscopic groups and base change C\/R.<\/strong><\/p>\n

Pacific J. Math,\u00a0 Vol. 110\u00a0 (1984),\u00a0 pp. 397 \u2013 415.\u00a0 here<\/a><\/p>\n

 <\/p>\n

Orbital integrals, endoscopic groups and L-indistinguishability for real groups.<\/strong><\/p>\n

Journ\u00e9es Automorphes<\/i>,\u00a0 Publ. Math. Univ. Paris VII,\u00a0 Vol. 15 (1983),\u00a0 pp. 135 \u2013 219.<\/p>\n

shelstadorbintegendoslindist<\/a><\/p>\n

 <\/p>\n

Embeddings of L-groups.<\/strong><\/p>\n

Canad. J. Math,\u00a0 Vol. 33 (1981),\u00a0 pp. 513 \u2013 558.<\/p>\n

Read here<\/a> or find pdf\u00a0here<\/a><\/p>\n

 <\/p>\n

Orbital integrals for GL<\/strong>2<\/strong><\/sub>(R). <\/strong><\/p>\n

Proc. Sympos. Pure Math, Vol. 33.1 (1979),\u00a0 pp. 107 \u2013 110.<\/p>\n

shelstadpspum331<\/a><\/p>\n

 <\/p>\n

Notes on L-indistinguishability (based on a lecture of R. Langlands). <\/strong><\/p>\n

Proc. Sympos. Pure Math, Vol. 33.2 (1979),\u00a0 pp. 193 \u2013 203.<\/p>\n

shelstadpspum332<\/a><\/p>\n

 <\/p>\n

Some character relations for real reductive algebraic groups.<\/strong><\/p>\n

Thesis, 58 pp.<\/p>\n

shelstadthesis<\/a><\/p>\n

\u201d \u2026 had proven in her thesis many pretty results on real groups.\u201d<\/em><\/p>\n

Corvallis proceedings, part 2, p. 162.<\/p>\n

****<\/p>\n

 <\/p>\n

OTHER PAPERS:<\/strong>\u00a0 either reprint is freely available online here<\/a> or here<\/a> or here<\/a><\/p>\n

or if joint with R. Langlands then there is a coauthor preprint\u00a0here<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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