Minor Summation Formula of Pfaffians

Masao Ishikawa, Masato Wakayama

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


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(Matq(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 languageEnglish
Pages (from-to)285-305
Number of pages21
JournalLinear and Multilinear Algebra
Issue number3
Publication statusPublished - Aug 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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