Another Proof of Gustafson’s $C_n$-type Summation Formula via ‘Elementary’ Symmetric Polynomials

Masahiko Ito

doi:10.2977/prims/1166642114

JournalsprimsVol. 42, No. 2pp. 523–549

Another Proof of Gustafson’s $C_{n}$ -type Summation Formula via ‘Elementary’ Symmetric Polynomials

Masahiko Ito
Aoyama Gakuin University, Kanagawa, Japan

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Abstract

We introduce new symmetric polynomials which induce a $q$ -difference equation associated with a basic hypergeometric sum of type $C_{n}$ investigated by Gustafson. Using them we give another proof for Gustafson’s $C_{n}$ -type summation formula.

Cite this article

Masahiko Ito, Another Proof of Gustafson’s $C_{n}$ -type Summation Formula via ‘Elementary’ Symmetric Polynomials. Publ. Res. Inst. Math. Sci. 42 (2006), no. 2, pp. 523–549

DOI 10.2977/PRIMS/1166642114