Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 740: Symmetric Functions

Not offered in 2017-2018.

 

Steven Sam (Spring 2017):

Introduction to theory of symmetric functions and their applications to algebra. This course should be of interest to those who have an interest in combinatorics, representation theory, and/or algebraic geometry. Among the basic topics we will cover:

  • Schur functions,
  • Robinson-Schensted-Knuth correspondence,
  • Littlewood-Richardson rule

For advanced topics, we will cover some subset of these possible topics:

  • basic connections to representation theory (ordinary representations of symmetric groups, polynomial representations of complex general linear groups),
  • Schubert calculus on Grassmannians,
  • Hall-Littlewood polynomials and other connections to representation theory (ordinary representations of general linear groups over finite fields, projective representations of symmetric groups).

Textbooks:

  • Richard Stanley, Enumerative Combinatorics Volume 2
  • I.G.Macdonald, Symmetric Functions and Hall Polynomials, second edition
credits: 
3 (N-A)
semester: 
InFrequent
prereqs: 
741

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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