Pfaffian Formulation of Schur's $Q$functions
Abstract
We introduce a Pfaffian formula that extends Schur's $Q$functions $Q_\lambda$ to be indexed by compositions $\lambda$ 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 $Q_\lambda$ 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.13137
 arXiv:
 arXiv:2405.13137
 Bibcode:
 2024arXiv240513137G
 Keywords:

 Mathematics  Combinatorics;
 05E05
 EPrint:
 29 pages