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J. Algebra 209
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Identities for classical group characters of nearly
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
and MacMahon (ex-)conjectures.
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