TY - JOUR
T1 - Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials
AU - Ishikawa, Masao
AU - Wakayama, Masato
N1 - Funding Information:
1Partially supported by Grant-in-Aid for Scientific Research Ministry of Education, Science and Culture of Japan. 2Partially supported by Grant-in-Aid for Scientific Research Ministry of Education, Science and Culture of Japan.
PY - 1999/10
Y1 - 1999/10
N2 - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.
AB - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.
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U2 - 10.1006/jcta.1999.2988
DO - 10.1006/jcta.1999.2988
M3 - Article
AN - SCOPUS:0000824310
SN - 0097-3165
VL - 88
SP - 136
EP - 157
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
IS - 1
ER -