Diana Shelstad


Recent and current work        Older work        Current teaching         Other

(publications, preprints, links, etc.)


Tempered endoscopy for real groups I: geometric transfer with canonical factors.

Contemporary Math,  Vol. 472  (2008),  pp. 215 – 246.

Preprint  pdf


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.

Preprint  pdf


Tempered endoscopy for real groups III: inversion of transfer and L-packet structure.

Representation Theory,  Vol. 12  (2008),  pp. 369 – 402.  here

Preprint (remark added, p. 48)  pdf


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.  pdf


A note on real endoscopic transfer and pseudo-coefficients.

Preprint (preliminary version,  Nov 2010),  6 pp.  pdf


Some results on endoscopic transfer.

Notes for Banff 2011 workshop on L-packets, 18 pp. pdf     Another abstract  pdf


On geometric transfer in real twisted endoscopy.

Annals of Math,  Vol. 176  (2012),  pp. 1919 – 1985.  here

Preprint (v. May 2012)   pdf


On splitting invariants and sign conventions in endoscopic transfer.

With R. Kottwitz.

Preprint (v. Jan 2012)  19 pp.  pdf     arXiv


Slides for talks:

here, Oct 2012: pdf   

here, May 2013: pdf   

here, May 2014: pdf* here  

*slide 15: normalize integrals with |D|1/2


On the structure of endoscopic transfer factors.

Accepted for publication.

Preprint (v. March 2015)  22 pp.  pdf     arXiv


On elliptic factors in real endoscopic transfer I.

Progress in Math 312, Birkhäuser (2015),  pp. 455 – 504.

Preprint (v. October 2015)   pdf     arXiv


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 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 available on request, 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 some early sources for the notion of transfer in Langlands Functoriality.

In preparation, preprint will be available shortly.

Invited paper for special volume dedicated to R. P. Langlands, Cambridge University Press, to be submitted for refereeing by April 2019.

From submitted brief summary, August 2018: "... we may ask what does transfer mean or even what does Langlands Functoriality mean. The two notions, whatever they are or should be, are intricately intertwined with each other. To get started, what are the objects we study? And then, what does it mean to transfer them? Where do functoriality principles come into play? After very limited remarks towards answers in some generality, we examine, also briefly, several concrete examples where we do have quite simple explicit answers. They do appear to be of interest and perhaps of a little influence in current research work on both Endoscopic Transfer and Transfer Beyond Endoscopy. ..."





Foundations of Twisted Endoscopy

Astérisque,  Vol. 255, 1999.

With R. Kottwitz.

Preprint, 180 pp. pdf      Errata (January 2012): see pdf


A formula for regular unipotent germs.

Astérisque,  Vol. 171 – 172 (1989),  pp. 275 – 277.

Preprint  pdf


Transfer and descent: some recent results.

Harmonic Analysis on Reductive Groups, Birkhäuser (1991),  pp. 297 – 304.

Preprint  pdf


Base change and a matching theorem for real groups.

Noncommutative Harmonic Analysis and Lie Groups, SLN 880 (1981),  pp. 425 – 482.

Preprint  pdf


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.

Preprint  pdf


Embeddings of L-groups.

Canad. J. Math,  Vol. 33 (1981),  pp. 513 – 558.

Read here or find pdf here


Orbital integrals for GL2(R).

Proc. Sympos. Pure Math, Vol. 33.1 (1979),  pp. 107 – 110.  pdf


Notes on L-indistinguishability (based on a lecture of R. Langlands).

Proc. Sympos. Pure Math, Vol. 33.2 (1979),  pp. 193 – 203.  pdf


Some character relations for real reductive algebraic groups.

Thesis, 58 pp.  pdf

" ... had proven in her thesis many pretty results on real groups."

Corvallis proceedings, part 2, p. 162.



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





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Spring 2019 teaching: Jan 22 - May 2

26:645:632:01  [Graduate] Algebra II   

21:640:238:Q1  Foundations of Modern Math  

26:645:799:01  Doctoral Dissertation & Research [1 student]  


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Recent course assignments

Fall 2018: 26:645:631:Q1  [Graduate] Algebra I

Fall 2018: 26:645:799:01 Doctoral Dissertation and Research

Spring 2018: 21:640:238:Q1  Foundations of Modern Math

Spring 2018: 26:645:736:01  Adv Topics in Rep Theory

Spring 2018: 26:645:799:01  Doctoral Dissertation & Research

Fall 2017: 21:640:238:Q1  Foundations of Modern Math

Fall 2017: 26:645:799:01  Doctoral Dissertation & Research

Spring 2017: 21:640:238:Q1  Foundations of Modern Math

Spring 2017: 21:640:435:01 Geometry I

Fall 2016: 21:640:238:Q1  Foundations of Modern Math

Spring 2016: 26:645:636:01 Lie Groups

Fall 2015: 21:640:311:01 Advanced Calculus I

Fall 2015: 26:645:612:01 Real Analysis II

Spring 2015: 26:645:632:01 Algebra II

Fall 2014: 21:640:491:Q1 Math Seminar

Fall 2014: 26:645:631:01 Algebra I 

Spring 2014: 21:640:156:01 Honors Calculus II   

Fall 2013: 21:640:155:01 Honors Calculus I

Fall 2013: 26:645:736:01 Adv Tpcs - Rep Theory

Fall 2013, Individual Study: 21:640:494:01

Spring 2013: 26:645:632:01 Algebra II

Spring 2013: 21:640:492:Q1 Math Seminar  info

Spring 2013, Individual Study: For Honors College  21:525:498:01





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