### 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 |
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Pages (from-to) | 285-305 |

Number of pages | 21 |

Journal | Linear and Multilinear Algebra |

Volume | 39 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 1 1995 |

Externally published | Yes |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## 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