Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities

Authors:
Masao Ishikawa;Masato Wakayama
Affiliations:
Department of Mathematics, Faculty of Education, Tottori University, Tottori, Japan;Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, Japan
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

Citing 5
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Two Variable Pfaffian Identities and Symmetric Functions

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Zeilberger's holonomic ansatz for Pfaffians

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Abstract

The initial purpose of the present paper is to provide a combinatorial proof of the minor summation formula of Pfaffians in [Ishikawa, Wakayama, Minor summation formula of Pfaffians, Linear and Multilinear Algebra 39 (1995) 285-305] based on the lattice path method. The second aim is to study applications of the minor summation formula for obtaining several identities. Especially, a simple proof of Kawanaka's formula concerning a q-series identity involving the Schur functions [Kawanaka, A q-series identity involving Schur functions and related topics, Osaka J. Math. 36 (1999) 157-176] and of the identity in [Kawanaka, A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups, Osaka J. Math. 38 (2001) 775-810] which is regarded as a determinant version of the previous one are given.