Sam Armon, ICERM 

Title: Super major index and Thrall’s problem

Abstract: A classical result in symmetric function theory relates the principal specialization of a Schur function to the major index statistic on standard Young tableaux. As a result, one can describe e.g. the graded $S_n$-decomposition of the coinvariant algebra, and the $S_n$-decomposition of the graded components of the free Lie algebra, in terms of the major index. We define a super analogue of the major index statistic which relates to the principal specialization of a supersymmetric Schur function, and use this new statistic to determine the $S_n$-decomposition of the bigraded components of the free Lie superalgebra. Joint work with Josh Swanson.