Announcements

Class cancelled Mon. Feb. 3 due to an AMS obligation in Washington, D.C.

Video from Zoom classes beginning Mon. Mar. 30 is / will be posted on eLC in the MATH8030 Course Content : Class Videos module.

Zoom office hour to be held at 9:55 am (after class ends) on Fri. Apr. 10.

Verma module
By Mathphysman - Mathematica, CC BY-SA 4.0, Link

Brief Syllabus

The course text is James E. Humphreys, Representations of Semisimple Lie Algebras in the BGG Category O, Graduate Studies in Mathematics 94, American Mathematical Society, 2008.

I hope to cover most of Chapters 0, 1, 3, 4.1-4.6, 4.11, 5.1-5.7, 7.1-7.7, 7.9, 7.12, 7.14, and selections from Chapter 8.

Nominally, grades will be based on homework, class attendance, and class participation. If you want to be evaluated in a different way, please email me a proposal.

Office hours (Boyd 601B): Drop-in MWF after 10:00. Exceptions: Algebra Seminar M 3:30-4:30; research meeting W 2:30-3:45; lunch 11:30-1:00. 

Course Notes (after Spring Break)

MATH8030_001.pdf

MATH8030_002.pdf

MATH8030_003.pdf

MATH8030_004.pdf

MATH8030_005.pdf

MATH8030_006.pdf

MATH8030_007.pdf

MATH8030_008.pdf

MATH8030_009.pdf

MATH8030_010.pdf

MATH8030_011.pdf

MATH8030_012.pdf

MATH8030_013.pdf

MATH8030_014.pdf

Homework

Do as many of the problems as you have time for. Feel free to do more if you want! Starred problems are especially important--they will be used later in the course. Double-starred are more difficult than average and are optional.

Assignment Due Date Problems
Asst. 1 Mon. 1/27 1.1, 1.3*
Asst. 2 Mon. 2/10 1.5, 1.9**
Asst. 3 Mon. 2/24 1.10*, 1.12, 1.13
Asst. 4 Mon. 3/30 3.1, 3.2, 3.4, 3.7
Asst. 5 Mon. 4/13 4.3, 4.6, 4.11
Asst. 6 Man. 4/27 5.3, 7.2, and the Exercise on p.108 of the class notes 004.

Links

Many corrections to Humphreys' book: http://people.math.umass.edu/~jeh/pub/bgg.pdf