Linearly Independent Products of Rectangularly Complementary Schur Functions
Abstract
Description
Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(mu^c), where mu and mu^c run over all (unordered) pairs of partitions which are complementary with respect to R.
Theorem: The self-complementary products, s(mu)^2 where mu=mu^c, are linearly independent of all other s(mu) s(mu^c).
Conjecture: The products s(mu) s(mu^c) are all linearly independent.
8 pages. Final version appearing in EJC. Formerly titled "A Theorem and a Conjecture on Rectangles and Schur Functions;" the section on the conjecture has been abbreviated and minor edits made throughout
8 pages. Final version appearing in EJC. Formerly titled "A Theorem and a Conjecture on Rectangles and Schur Functions;" the section on the conjecture has been abbreviated and minor edits made throughout