Linearly Independent Products of Rectangularly Complementary Schur Functions
Abstract
Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(muc), where mu and muc run over all (unordered) pairs of partitions which are complementary with respect to R. Theorem: The self-complementary products, s(mu)2 where mu=muc, are linearly independent of all other s(mu) s(muc). Conjecture: The products s(mu) s(muc) are all linearly independent.
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