Pieri Rule for GQs Computed via Strict Decomposition Tableaux

Abstract

$GQ$ functions are symmetric functions indexed by strict partitions that represent $K$-theoretic Schubert classes in the Lagrangian Grassmannian. Buch and Ravikumar proved a Pieri rule for expanding $G{Q}_{\hat{I}}»\cdot G{Q}_p$ in terms of $GQ$s via certain shifted skew tableaux. In this paper we identify an alternative family of shifted tableaux that enumerates this Pieri rule. This partially resolves a conjecture from previous work that these tableaux enumerate the expansion of $G{Q}_{\hat{I}}»\cdot G{Q}_{\ddot{I}}„$ in terms of $GQ$s where $\ddot{I}„$ is a trapezoid shape.

15 pages, Revision: fixed typo in tableaux in remark 3.24