Stanley symmetric functions and Peterson algebras

Abstract

These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems.

29 pages

References in corpus (5)

• Positroid varieties I: juggling and geometry
• Dual equivalence graphs and a combinatorial proof of LLT and Macdonald positivity
• The Murnaghan-Nakayama rule for k-Schur functions
• Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras
• Gromov-Witten invariants for G/B and Pontryagin product for ΩK

Cited by in corpus (6)

• Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures
• Symmetries on the lattice of $k$-bounded partitions
• Combinatorial expansions for families of non-commutative k-Schur functions
• Coxeter-Knuth graphs and a signed Little map for type B reduced words
• Diagrams of affine permutations, balanced labellings, and symmetric functions
• The down operator and expansions of near rectangular k-Schur functions