Sabine J Lang

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.