Séminaire Lotharingien de Combinatoire, B81k (2020), 50 pp.
Soichi Okada
A Generalization of Schur's P- and Q-Functions
Abstract.
We introduce and study a generalization of Schur's P-/Q-functions
associated with a polynomial sequence,
which can be viewed as ``Macdonald's ninth variation'' for P-/Q-functions.
This variation includes as special cases Schur's P-/Q-functions,
Ivanov's factorial P-/Q-functions and the t=-1 specialization of Hall-Littlewood functions
associated with the classical root systems.
We establish several identities and properties such as generalizations
of Schur's original definition of Schur's Q-functions, a Cauchy-type identity,
a generalization of the Józefiak-Pragacz-Nimmo formula for skew Q-functions,
and a Pieri-type rule for multiplication.
Received: April 6 2019.
Accepted: May 18, 2020.
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