2015/12/15 by Avinash J. Dalal, Dalal, Avinash J.
Mathematics · #05E05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E05
paper · pdf · doi:10.48550/arxiv.1512.04627
17 pages, 3 tables
arxiv created 2015/12/15 · arxiv updated 2015/12/16
The branching of (k-1)-Schur functions into k-Schur functions was given by Lapointe, Lam, Morse and Shimozono as chains in a poset on k-shapes. The k-Schur functions are the parameterless case of a more general family of symmetric functions over Q(t), conjectured to satisfy a k-branching formula given by weights on the k-shape poset. A concept of a (co)charge on a k-tableau was defined by Lapointe and Pinto. Although it is not manifestly positive, they prove it is compatible with the k-shape poset for standard k-tableau and the positivity follows. Morse introduced a manifestly positive notion of affine (co)charge on k-tableaux and conjectured that it matches the statistic of Lapointe-Pinto. Here we prove her conjecture and the positivity of k-(co)charge for semi-standard tableaux follows.