Linearly Independent Products of Rectangularly Complementary Schur Functions

Michael Kleber

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arXiv · math/0209136

Linearly Independent Products of Rectangularly Complementary Schur Functions

Michael Kleber

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Abstract

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.

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BibTeX RIS

Michael Kleber. 2002-10-04. Linearly Independent Products of Rectangularly Complementary Schur Functions. https://arxiv.org/abs/math/0209136

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