2019/04/29 by Ming Fang, Kay Jin Lim, Fang, Ming +3
Mathematics · Chemistry · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.1904.13040
Let G be a connected reductive algebraic group over an algebraically closed\nfield of characteristic p>0, \Δ(\λ) denote the Weyl module of G\nof highest weight \λ and \ι\λ,\μ:\Δ(\λ+\μ)\→\n\Δ(\λ)\⊗\Δ(\μ) be the canonical G-morphism. We study the\nsplit condition for \ι\λ,\μ over \ℤ(p), and apply\nthis as an approach to compare the Jantzen filtrations of the Weyl modules\n\Δ(\λ) and \Δ(\λ+\μ). In the case when G is of type\nA, we show that the split condition is closely related to the product of\ncertain Young symmetrizers and, under some mild conditions, is further\ncharacterized by the denominator of a certain Young's seminormal basis vector.\nWe obtain explicit formulas for the split condition in some cases.\n