TY - JOUR
T1 - Minor Summation Formula of Pfaffians
AU - Ishikawa, Masao
AU - Wakayama, Masato
N1 - Funding Information:
'Partially supported by Inoue Foundation for Science and partially supported by Grant-in Aid for Scientific Research No. 06740027, the Ministry of Education, Science and Culture of Japan. 'Partially supported by Grant-in Aid for Scientific Research No. 05640190 and on Priority Areas No. 05230045, the Ministry of Education, Science and Culture of Japan.
PY - 1995/8/1
Y1 - 1995/8/1
N2 - 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.
AB - 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.
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U2 - 10.1080/03081089508818403
DO - 10.1080/03081089508818403
M3 - Article
AN - SCOPUS:84949693968
VL - 39
SP - 285
EP - 305
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 3
ER -