Identities for classical group characters of nearly rectangular shape. (English) Zbl 0914.20038
The author derives several identities involving irreducible characters of the classical groups – the general linear, the symplectic and the orthogonal groups. All of the identities feature characters that are indexed by shapes that are “nearly” rectangular, i.e., the shapes are rectangular but for one row or column that might be shorter than the others. As applications, the author also proves new results in plane partitions and tableaux enumeration. The tableaux descriptions by De Concini, Procesi, Lakshmibai, Musili and Seshadri play an important role in the proof of these results.
Reviewer: V.Lakshmibai (Boston)
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 05E10 | Combinatorial aspects of representation theory |
Keywords:
rectangular shapes; identities; irreducible characters; classical groups; orthogonal groups; plane partitions; tableaux enumerationReferences:
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