Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.
A Modified Greaves--Jing--Zhu Operator and a Shifted $t$-Gessel Formula
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
The recent work of Greaves, Jing, and Zhu gives an operator construction for the $t$-Schur functions and the $t$-Schur measure. Motivated by their construction, we consider the same type of vertex operator on the odd power-sum ring. Its Fourier modes generate a family of symmetric functions indexed by strict partitions, which we call shifted $t$-Schur functions. These functions specialize to Schur $Q$-functions at $t=0$. We derive a two-row formula, a Pfaffian Giambelli formula, a Cauchy identity, and a finite shifted Gessel-type formula. This note is intended as a first step toward further study of the odd-operator analogue of the Greaves--Jing--Zhu construction.
years
2026 4verdicts
UNVERDICTED 4representative citing papers
Defines shifted t-Schur weight via modified odd operator on strict partitions, derives normalization, Pfaffian correlation kernel, Fredholm Pfaffian for largest part, and size cumulants, with positive measure for t equals negative q.
Computes the scalar factor in mixed products of modified Greaves-Jing-Zhu operators on the odd power-sum ring for parameters t and s, with explicit forms, recurrences, and a special case s=t^M linking to signed principal specializations of one-row Schur Q-functions.
Derives transition matrices and proves Schur Q-positivity plus reciprocity for cyclotomic specializations of shifted t-Schur functions.
citing papers explorer
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A Two-Color Lift of the Shifted $t$-Schur Measure
Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.