Kronecker Products, Characters, Partitions, and the Tensor Square Conjectures
نویسندگان
چکیده
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups Sn contain all irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of characters, and use combinatorics of rim hook tableaux combined with known results on unimodality of certain partition functions. We also present connections and speculations on random characters of Sn.
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تاریخ انتشار 2013