Identities for classical group characters of nearly rectangular shape

JOURNAL OF ALGEBRA

卷:209

Article

Krattenthaler, C

关键词: Schur functions;    general linear characters;    symplectic characters;    orthogonal characters;    characters of Lie groups;    tableaux;    plane partitions;    Littlewood-Richardson rule;    restriction rules;   

DOI  :  10.1006/jabr.1998.7531

来源: Elsevier

【 摘 要 】

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All of 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. (C) 1998 Academic Press.

【 授权许可】

Free