9
$\begingroup$

I am planning in running a Ph.D. student seminar next year on representation theory in the spirit of MIT Kan's Seminar where students give lectures on classical articles on representation theory that are typically not covered in a first course but that can none-the-less be covered in one week or so. I would like to amass a list of 12-20 articles or book chapters that should compose such a seminar. Examples would be

Demazure Inventiones 33 (1976) 271-272 "A very simple proof of Bott's theorem",

A. Beilinson, J. Bernstein, Localization de g-modules, C.R. Acad. Sci. Paris, 292 (1981), 15-18.

Chapter 4 of Chriss-Ginzburg "Representation Theory and Complex Geometry".

and non-examples should be the geometric Satake isomorphism or Zhu's modularity of characters of vertex algebras.

I am not sure if this question goes here or not, but ME seemed like the wrong place to ask. Since I found similar questions here like A request for suggestions of advanced topics in representation theory and A learning roadmap for Representation Theory I figured it was alright.

Edit: as Tobias and Jim asked for background, I would want this class to be a second year graduate class in representation theory for students with different backgrounds, however, in general I would require students to be familiar with the standard first year classes like finite dimensional Lie algebras over $\mathbb{C}$ (say Jim's GTM book), finite dimensional compact groups (as in the first chapters of Knapp's Lie groups beyond an introduction), the basics of algebraic geometry as in the first 3 chapters of Hartshorne. And hopefully some knowledge of differentiable manifolds as in Warner and/or complex geometry as in Wells.

The focus of the seminar may/can vary from year to year, as does Kan's seminar, I myself would rather be more about geometric representations as the list supplied suggest. Finally the definition of classical is left intentionally vague as I would want it to be "those articles that most in the field have read or should have read".

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Could you elaborate a bit on the topic you mean to cover? I mean, will it be of a mainly algebraic or geometric flavour? And how "classical" do they need to be (i.e. how to judge if a text is classic or not?). $\endgroup$
    – Tobias Kildetoft
    Commented Dec 8, 2015 at 11:31
  • $\begingroup$ To reinforce what Tobias says, I'd wonder what background the students need to have. Some of the older Kostant or Steinberg papers have accessible parts but tend to be fairly long and perhaps over-dependent on prior knowledge. There is also the ubiquitous "Lang's theorem" for algebraic groups in prime characteristic; the original proof is short but set in an old-fashioned algebraic geometry language, while the later version by Steinberg is an improvment but not really modern. Lots of possible directions. $\endgroup$
    – Jim Humphreys
    Commented Dec 8, 2015 at 20:15

2 Answers 2

Reset to default
3
$\begingroup$

Bertram Kostant, Lie Algebra Cohomology and the Generalized Borel-Weil Theorem, Ann. of Math., 74, (1961), No. 2, 329-387

Improve this answer
$\endgroup$
1
  • $\begingroup$ You are welcome. :) It's a great paper and it still bears fruit today. See e.g. arxiv.org/abs/1208.5453 $\endgroup$
    – Vít Tuček
    Commented Dec 8, 2015 at 22:34
2
$\begingroup$

Bernšteĭn, I. N.; Gelʹfand, I. M.; Gelʹfand, S. I. Differential operators on the base affine space and a study of $\mathfrak{g}$-modules. Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), pp. 21–64. Halsted, New York, 1975.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .