A Shifted $t$-Schur Weight from the Modified Odd Operator

S. -J. Lee

A Shifted $t$-Schur Weight from the Modified Odd Operator

Combinatorics 2026-07-02 v1

Authors: S. -J. Lee

Abstract

We study the one-time weight on strict partitions obtained from the modified odd Greaves--Jing--Zhu operator. The shifted $t$ -Schur functions generated by this operator are obtained from the classical Schur $Q$ -functions by the plethystic substitution $X\mapsto X-tX$ . Thus the corresponding weight $\lambda \longmapsto \mathcal Q_\lambda(X;t)P_\lambda(Y)$ is a shifted Schur weight with a virtual first alphabet. We give its normalization, its Pfaffian correlation kernel, its Fredholm Pfaffian for the largest part, and its size cumulants. For $t=-q$ with $q\geq 0$ the virtual alphabet becomes the positive alphabet $X+qX$ , giving a genuine probability measure. This positive specialization is the one-time marginal of the two-color lift considered in a companion note.

Cite

@article{arxiv.2607.01839,
  title  = {A Shifted $t$-Schur Weight from the Modified Odd Operator},
  author = {S. -J. Lee},
  journal= {arXiv preprint arXiv:2607.01839},
  year   = {2026}
}