Colloquium: Schur-like Bases of QSym and NSym: Properties of the Shin Functions

Spencer Daugherty, NC State
Thursday, 10/19, 11am, in Manchester 016

Schur-like Bases of QSym and NSym: Properties of the Shin Functions

Abstract: A Schur-like basis of the noncommutative symmetric functions is one whose commutative image is the Schur basis of the symmetric functions. The canonical Schur-like bases of NSym are the immaculate basis, the shin basis, and the Young noncommutative Schur basis, each of which reflects the properties of the Schur functions in interesting and surprisingly different ways. For each of these bases, we will discuss tableaux interpretations, various types of multiplication rules, and dual bases in the quasisymmetric functions. We will then present new results on the shin functions including a creation operator and Jacobi-Trudi rule for certain cases, along with observations about the multiplicative structure.