## Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. (arXiv:1804.04514v1 [math.CO])

We show that, for a certain class of partitions and an even number of
variables of which half are reciprocals of the other half, Schur polynomials
can be factorized into products of odd and even orthogonal characters. We also
obtain related factorizations involving sums of two Schur polynomials, and
certain odd-sized sets of variables. Currently, we do not have
representation-theoretic interpretations of any of the factorizations. Our
results generalize the factorization identities obtained by Ciucu and
Krattenthaler (Advances in combinatorial mathematics, 39-59, 2009) for
partitions of rectangular shape. We observe that if, in some of the results,
the partitions are taken to have rectangular or double-staircase shapes and all
of the variables are set to 1, then factorization identities for numbers of
certain plane partitions, alternating sign matrices and related combinatorial
objects are obtained.查看全文