UC Berkeley

In 2001, Lapointe, Lascoux, and Morse discovered a class of symmetric functions called k-Schur functions. These functions have many properties similar to Schur functions and were motivated by a conjectured refinement of the Macdonald positivity conjecture. We describe a representation-theoretic model for k-Schur functions by studying the combinatorics of special pairs of partitions called skew-linked partitions. En route we also study nonnegative integer matrices with specified row and column sums. These data allow us to construct "small" modules that are generalizations of

Garsia-Procesi modules. We describe properties of k-Schur functions that can be deduced from these modules.