Enumeration of symmetry classes of alternating sign matrices and characters of classical groups

被引：0
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作者：
Okada, Soichi [1 ]
机构：
[1] Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
来源：
Journal of Algebraic Combinatorics | 2006年 / 23卷 / 01期
关键词：
An alternating sign matrix is a square matrix with entries 1; 0 and -1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate in sign along each row and each column. To some of the symmetry classes of alternating sign matrices and their variations; G. Kuperberg associate square ice models with appropriate boundary conditions; and give determinant and Pfaffian formulae for the partition functions. In this paper; we utilize several determinant and Pfaffian identities to evaluate Kuperberg's determinants and Pfaffians; and express the round partition functions in terms of irreducible characters of classical groups. In particular; we settle a conjecture on the number of vertically and horizontally symmetric alternating sign matrices (VHSASMs). © Springer Science + Business Media; Inc; 2006;
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页码：43 / 69
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