Hyperdeterminantal expressions for Jack functions of rectangular shapes

JOURNAL OF ALGEBRA

卷:320

Article

Matsumoto, Sho

关键词: Jacobi-Trudi formula;    hyperdeterminant;    Jack function;    Schur function;    Toeplitz determinant;    pfaffian;   

DOI  :  10.1016/j.jalgebra.2007.09.013

来源: Elsevier

【 摘 要 】

We derive a Jacobi-Trudi type formula for Jack functions of rectangular shapes. In this formula, we make use of a hyperdeterminant, which is Cayley's simple generalization of the determinant. In addition, after developing the general theory of hyperdeterminants, we give summation formulas for Schur functions involving hyperdeterminants, and evaluate Toeplitz type hyperdeterminants by using Jack function theory. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free