Representation theory reading group

Spring 2019: Tuesdays at 1pm in LCB loft

January 18 Adam Brown Introduction to reductive algebraic groups.
January 25 Qixian (Cameron) Zhao Reductive groups over finite fields.
February 1 Jenny Kenkel The Hecke algebra.
February 15 Adam Brown The Hecke algebra, continued.
February 26 -- discussion -- Principal series representations.
March 5 -- discussion -- Flag varieties.

Main reference for Spring 2019:
  • Notes from 2018 WARTHOG summer school, available here

Fall 2018: Tuesdays at 3:10pm in JWB 108.

September 11/td> Adam Brown Introduction.
September 18 Qixian (Cameron) Zhao Linear algebra background. Representations of finite groups.
September 25 Qixian (Cameron) Zhao Linear algebra background, continued.
October 2 Sam Swain Decomposition of representations of finite groups into direct sums of irreducibles, character theory.
October 16 Faith Pearson Representations of the symmetric group.
October 30 Sabine Lang Double centralizer theorem and examples.
November 6 Chengyu Du Proof of Schur-Weyl duality.
November 13 Jenny Kenkel Determinantal rings and applications to commutative algebra.
November 20 Peter McDonald Geometric picture: Springer correspondence.
November 27 Adam Brown Physics II for computer sciences students

Suggested references for Fall 2018:
  • The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric functions, by Bruce E. Sagan
  • Young Tableaux, by William Fulton
  • Representation theory, by William Fulton and Joe Harris
  • Abstract algebra, by David S. Dummit and Richard Foote
  • Lecture notes by Pavel Etingof, available here

The notes from the Fall 2018 reading group are now available.