Minor Summation Formula of Pfaffians

Masao Ishikawa; Masato Wakayama

doi:10.1080/03081089508818403

Minor Summation Formula of Pfaffians

Masao Ishikawa, Masato Wakayama

Research output: Contribution to journal › Article

42 Citations (Scopus)

Abstract

In this paper we establish a formula involving Pfaffıans for a certain weighted sum of minors of an arbitrary given matrix. First we find a formula where the sum ranges for all columns, and secondly we obtain a formula where the sum ranges for both all rows and columns as the application of the first one. The first formula is stated in the framework of quantum matrix algebra A(Mat_q(m, n)). These sums are weighted by “sub-Pfaffıans” of any given (q-)skew symmetric matrices. In the last section we provide an application of the minor summation formula to the generating functions of shifted tableaux.

Original language	English
Pages (from-to)	285-305
Number of pages	21
Journal	Linear and Multilinear Algebra
Volume	39
Issue number	3
DOIs	https://doi.org/10.1080/03081089508818403
Publication status	Published - Aug 1 1995
Externally published	Yes

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ASJC Scopus subject areas

Algebra and Number Theory

Cite this

Ishikawa, M., & Wakayama, M. (1995). Minor Summation Formula of Pfaffians. Linear and Multilinear Algebra, 39(3), 285-305. https://doi.org/10.1080/03081089508818403

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Access to Document

10.1080/03081089508818403