##### This material has been published in Advances in Combinatorial Mathematics:
Proceedings of the Waterloo Workshop in Computer Algebra 2008,
I. Kotsireas, E. Zima (eds.), Springer-Verlag, 2010, pp. 39-60,
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##
Mihai Ciucu
and Christian Krattenthaler

# A factorization theorem for classical group characters, with
applications to plane partitions and rhombus tilings

### (19 pages)

**Abstract.**
We prove that a Schur function of rectangular shape (*M*^{n})
whose
variables are specialized to
*x*_{1},*x*_{1}^{-1},...,*x*_{n},*x*_{n}^{-1}
factorizes into a product of two odd orthogonal characters of
rectangular shape, one of which is evaluated at
-*x*_{1},...,-*x*_{n}, if
*M* is even, while it factorizes into a product of a symplectic
character and an even orthogonal
character, both of rectangular shape, if *M* is odd.
It is furthermore shown
that the first factorization implies a factorization theorem for
rhombus tilings of a hexagon, which has an equivalent formulation in
terms of plane partitions. A similar factorization theorem is proven
for the sum of two Schur functions of respective rectangular shapes
(*M*^{n}) and (*M*^{n-1}).

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