A Generalization of Schur's $P$- and $Q$-Functions

Abstract

We introduce and study a generalization of Schur's $P$-/$Q$-functions associated to 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 to the classical root systems. We establish several identities and properties such as generalizations of Schur's original definition of Schur's $Q$-functions, Cauchy-type identity, Józefiak--Pragacz--Nimmo formula for skew $Q$-functions, and Pieri-type rule for multiplication.

55 pages

References in corpus (1)

• Pfaffian Formulas and Schur Q-Function Identities

Cited by in corpus (4)

• Pfaffian Formulas and Schur Q-Function Identities
• Symplectic Q-functions
• Expanding K-theoretic Schur Q-functions
• Ninth variation of classical group characters of type A-D and Littlewood identities