
John Maxwell Campbell

Karen Feldman

Jennifer Light

Pavel Shuldiner

Yan Xu
Keywords:
Noncommutative symmetric functions, Pieri rules, Schur basis
Abstract
Recent research on the algebra of noncommutative symmetric functions and the dual algebra of quasisymmetric functions has explored some natural analogues of the Schur basis of the algebra of symmetric functions. We introduce a new basis of the algebra of noncommutative symmetric functions using a right Pieri rule. The commutative image of an element of this basis indexed by a partition equals the element of the Schur basis indexed by the same partition and the commutative image is $0$ otherwise. We establish a rule for rightmultiplying an arbitrary element of this basis by an arbitrary element of the ribbon basis, and a MurnaghanNakayamalike rule for this new basis. Elements of this new basis indexed by compositions of the form $(1^n, m, 1^r)$ are evaluated in terms of the complete homogeneous basis and the elementary basis.