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arXiv · 2405.13137

Pfaffian Formulation of Schur's $Q$-functions

John Graf·Naihuan Jing
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Abstract

We introduce a Pfaffian formula that extends Schur's $Q$-functions $Q_λ$ to be indexed by compositions $λ$ with negative parts. This formula makes the Pfaffian construction more consistent with other constructions, such as the Young tableau and Vertex Operator constructions. With this construction, we develop a proof technique involving decomposing $Q_λ$ into sums indexed by partitions with removed parts. Consequently, we are able to prove several identities of Schur's $Q$-functions using only simple algebraic methods.

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John Graf, Naihuan Jing. 2024-05-21. Pfaffian Formulation of Schur's $Q$-functions. https://doi.org/10.1016/j.jalgebra.2025.02.002

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