MY RESEARCH
CURRENT and RECENT
(publications, preprints, links, etc.)
On some early sources for the notion of transfer in Langlands Functoriality
Part I: An Overview with Examples
The Genesis of the Langlands Program
London Mathematical Society Lecture Note Series 467, Cambridge, 2021, pp. 387 – 400.
shelstadearlysourcestransferPART1
PART 2 is in preparation and will be submitted elsewhere.
On stable transfer for real groups.
has new title:
Beyond Endoscopy: an approach to stable-stable transfer at
the archimedean places.
“This 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. A base change result for C/R is included.”
A preprint for Part A will be posted as soon as available.
“Part 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.”
On elliptic factors in real endoscopic transfer II, in preparation.
“A central underlying theme in endoscopic transfer is Waldspurger’s 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’ envisioned Beyond Endoscopy program for a connected reductive group defined over a number field.”
On the structure of endoscopic transfer factors.
Representation Theory, Automorphic Forms, and Complex Geometry
International Press, Somerville, MA, 2020, pp. 81 – 105.
shelstadstructureendofactors arXiv
On elliptic factors in real endoscopic transfer I.
Progress in Math 312, Birkhäuser (2015), pp. 455 – 504.
Slides for talks:
here, Oct 2012: shelstad24slides
here, May 2013: shelstadtalkschmidconf
here, May 2014: pdf here Slide15: normalize integrals with |D|1/2
On splitting invariants and sign conventions in endoscopic transfer.
With R. Kottwitz, 19 pp.
On geometric transfer in real twisted endoscopy.
Annals of Math, Vol. 176 (2012), pp. 1919 – 1985. here
Some results on endoscopic transfer.
Notes for Banff 2011 workshop on L-packets, 18 pp.
ShelstadNotesJune2011 See also shelstadabstract121511
A note on real endoscopic transfer and pseudo-coefficients.
Preprint, preliminary version, Nov 2010, 6 pp.
Examples in endoscopy for real groups.
Notes for talks, Banff 2008 summer school and workshop on stable trace formula,
Galois representations and Shimura varieties, 59 pp.
Tempered endoscopy for real groups III: inversion of transfer and L-packet structure.
Representation Theory, Vol. 12 (2008), pp. 369 – 402. here
shelstadtempend3 Remark added, p. 48
Tempered endoscopy for real groups II: spectral transfer factors.
自守形式与Langlands纲领 Automorphic forms and the Langlands Program
Higher Education Press/ International Press, 2009/ 2010, pp. 236 – 276.
shelstadtempend2
Tempered endoscopy for real groups I: geometric transfer with canonical factors.
Contemporary Math, Vol. 472 (2008), pp. 215 – 246.
SOME OLDER
Foundations of Twisted Endoscopy
Astérisque, Vol. 255, 1999.
With R. Kottwitz.
KottwitzShelstadFoundationsTwistedEndoscopy
Errata (January 2012) in KSsplittingsigns
A formula for regular unipotent germs.
Astérisque, Vol. 171 – 172 (1989), pp. 275 – 277.
shelstadformularegularunipotentgerms
Transfer and descent: some recent results.
Harmonic Analysis on Reductive Groups, Birkhäuser (1991), pp. 297 – 304.
shelstadtransferdescentresults
Base change and a matching theorem for real groups.
Noncommutative Harmonic Analysis and Lie Groups, SLN 880 (1981), pp. 425 – 482.
shelstadrealbasechangefirstattempt
Endoscopic groups and base change C/R.
Pacific J. Math, Vol. 110 (1984), pp. 397 – 415. here
Orbital integrals, endoscopic groups and L-indistinguishability for real groups.
Journées Automorphes, Publ. Math. Univ. Paris VII, Vol. 15 (1983), pp. 135 – 219.
Embeddings of L-groups.
Canad. J. Math, Vol. 33 (1981), pp. 513 – 558.
Orbital integrals for GL2(R).
Proc. Sympos. Pure Math, Vol. 33.1 (1979), pp. 107 – 110.
Notes on L-indistinguishability (based on a lecture of R. Langlands).
Proc. Sympos. Pure Math, Vol. 33.2 (1979), pp. 193 – 203.
Some character relations for real reductive algebraic groups.
Thesis, 58 pp.
” … had proven in her thesis many pretty results on real groups.”
Corvallis proceedings, part 2, p. 162.
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OTHER PAPERS: either reprint is freely available online here or here or here
or if joint with R. Langlands then there is a coauthor preprint here