Generalized Sylvester Formulas and skew Giambelli Identities

2017/04/09 by Soichi Okada, Okada, Soichi · 1 citation
Mathematics · Physics and Astronomy · #05E05 #15A15 #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.1704.02585

openalex publication_date 2017/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a common generalization of two types of Sylvester formulas for compound determinants and its Pfaffian analogue. As applications, we give generalizations of the Giambelli identity to skew Schur functions and the Schur identity to Schur's skew Q-functions.

Cited by

• Quadratic relations for ninth variations of Schur functions and application to Schur multiple zeta functions

Related

• New determinant formulas of Giambelli-type for Schur multiple zeta-functions and their applications
• Determinantal and Pfaffian identities for ninth variation skew Schur\n functions and Q-functions
• A Hopf algebraic approach to Schur function identities
• Generalizations of Sylvester's determinantal identity
• Division and the Giambelli Identity