Character Polynomials and the Restriction Problem

Character polynomials are used to study the restriction of a polynomial representation general linear group its subgroup permutation matrices. A simple formula is obtained for computing inner products class functions given by character polynomials. symmetric and alternating tensors computed using generating with Eulerian factorizations. These compute Weyl modules, which exhibit duality. By taking modules Specht stable coefficients easily computed. Generating dimensions invariants in obtained. Partitions two rows, columns, hook partitions whose have non-zero vectors invariant under characterized. reformulation problem terms functor from category strict functors finitely generated FI-modules