近矩形典型群特征标的恒等式
Identities for classical group characters of nearly rectangular shape
摘要：
我们得到几个身份，功能不可约字符的一般线性，辛，正交和特殊的正交群。所有的标识都以“近似”矩形的形状为索引的字符为特征，我们的意思是除了一行或一列可能比其他行或列短之外，这些形状都是矩形。作为应用，我们证明了新的结果，在平面分区和tableaux枚举，包括新的改进的Bender-Knuth和MacMahon（前）代数。
英文摘要：
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly" rectangular, by which we mean that the shapes are rectangles except for one row or column that might be shorter than the others. As applications we prove new results in plane partitions and tableaux enumeration, including new refinements of the Bender-Knuth and MacMahon (ex-)conjectures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
