Office hours:: MW2-3 and by appointment
Office: APM 5256, tel. 534-2734
Email: hwenzl@ucsd.edu
Prerequisites: A solid understanding and familiarity with basic concepts in algebra (groups, homomorphisms etc) and analysis (convergence, norms) as well as a good understanding of linear algebra. Ask me if in doubt.
Material: This is a continuation of Lie Groups 251B, taught in Winter 2022. We will first concentrate on the representation theory of semisimple Lie agebras. This will include a proof of the character formula, decomposition of tensor products of representations and duality theorems (such as Schur-Weyl duality, Howe duality). Further topics may include real non-compact Lie groups, symmetric spaces and q-deformations of universal enveloping algebras, known as quantum groups. There will not be a fixed course book. The books and lecture notes listed below should cover most of the material of the course. For material not covered in these books, we plan to make other resources available.
Some books/lecture notes related to the course:
Lie Groups, Lie Algebras, And Representations : An Elementary Introduction, Brian C. Hall (electronic copy available from our library)
Introduction to Lie Algebras and Representation Theory, James E. Humphreys, Springer (electronic copy available from our library)
Representation Theory. A First Course, Graduate Texts in Mathematics 129, Joe Harris and William Fulton, Springer (electronic copy available from our library)
Some lecture notes for this course:
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Below are some notes for certain topics of the course
Here are some problems and remarks concerning this course: