# 18.757 Representations of Lie Groups not-really-a-web-page

• Meeting time: Tuesday/Thursday 1-2:30, Room 2-143
• Text: Anthony Knapp, Lie Groups Beyond an Introduction.

David Vogan, 2-243

dav@math.mit.edu

x3-4991

Office hours Monday and Tuesday 3:00-4:00 (or any time).

Blurb describing course pdf

correction to proof given in class 2/12/13 for Jacobson density theorem.

Original version of problems due Tuesday, February 12. Corrected (changing exponent k+2 to k. Solutions.

Problems due Thursday, February 21. (Intended to be exactly as assigned in class Thursday, February 14; just printed here for clarity.) Solutions.

Problems due Tuesday, February 26. (Intended to be exactly as assigned in class Thursday, February 21; just printed here for clarity.) Solutions.

Problems due Thursday, March 14. I originally assigned this as one problem due about two weeks ago, and never fulfilled a promise to write it up in detail. I believe that the first three problems written here are very close to what was assigned in class, so that if you already wrote a solution to that, it should serve as a solution to this. The fourth problem here is new. Solutions.

Problems due Tuesday, April 9. Slightly modified from assignment in class April 2: first question there is now answered in the notes on classical groups, and a new question has been added intended as a step toward one of the original ones. Solutions (so far missing a solution to 2(e)).

Solution to the problem due Thursday, April 18.

Problems due Thursday, May 2. Solutions.

Problem set 8, due Tuesday May 14, is to describe completely the branching law from SU(2) to the binary icosahedral group I~ of order 120. This means that you should say how to write the irreducible m-dimensional representation of SU(2) as a combination of the nine irreducible representations \pi_0 = trivial, \pi_1, ..., \pi_8 = tautological. The labeling was explained in class. The McKay notes give a bijection between the nontrivial irreducibles and the simple roots of E_8; those simple roots are numbered 1--8 by Bourbaki. Solution.

Notes on the McKay correspondence pdf. Late May 7: the notes are now more or less complete, although missing a lot of material I'd like to include.

Notes on the weights of representations of compact groups pdf

Notes on compact classical groups pdf

Notes on representations of SL(2,R) pdf ps

Notes on harmonic analysis on compact groups pdf ps

Notes on integration on homogeneous spaces pdf ps

Early problems assigned in 2007, and more problem sets from 2007.