Jan 17 
What are symmetric functions? 7.1
Polynomial representations of general linear groups 7.A2
Partitions 7.2

Jan 19 
Monomial symmetric functions 7.3
Elementary symmetric functions 7.4


Jan 24 
The involution ω 7.6
Complete homogeneous symmetric functions 7.5
Power sum symmetric functions 7.7

Jan 26 
Scalar product 7.9
Some representation theory
Semistandard Young tableaux 7.10 

Jan 31 
Schur functions 7.10
RSK algorithm 7.11

Feb 2 
RSK algorithm and corollaries 7.127.14
Classical definition of Schur functions 7.15


Feb 7 
JacobiTrudi identity 7.16
Summary of representation theory of finite groups

Feb 9 
Representations of the symmetric group 7.18 

Feb 14 
MurnaghanNakayama rule 7.17

Feb 16 
SchurWeyl duality
Grassmannians and Schubert decomposition 

Feb 21 
Schubert varieties
Review of cohomology ring

Feb 23 
Schubert calculus 

Feb 28 
Chern roots/classes
Lines on a cubic surface

Mar 2 
Formulas for number of SYT and SSYT 

Mar 7 
LittlewoodRichardson coefficients
Combinatorics of finite abelian pgroups

Mar 9 
Hall algebras and Hall polynomials 

Mar 14 
HallLittlewood symmetric functions, definitions

Mar 16 
HallLittlewood symmetric functions, Pieri rule
Connection to Hall polynomials 

Mar 21  Spring break  no class 
Mar 23  Spring break  no class 

Mar 28  HallLittlewood function identities 
Mar 30  tdeformation of JacobiTrudi identity
tdeformation of inner product 

Apr 4  Schur Qfunctions

Apr 6  Projective representation theory 

Apr 11  Clifford algebras

Apr 13  Guest lecture: Daniel Erman 

Apr 18  no class

Apr 20  The basic spin representation 

Apr 25  Frobenius characteristic map for projective representations

Apr 27  Schur Qfunctions: wrapup 

May 2  no class 
May 4  Guest lecture: Jordan Ellenberg 