2013/09/02 by Chuck Hague, Hague, Chuck
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1309.0468
openalex publication_date 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a semisimple algebraic group over an algebraically closed field of\npositive characteristic p. Generalizing the construction of the PBW filtration\non Weyl modules for G we construct a G-stable filtration on tensor products of\nWeyl modules which we call the induced PBW filtration. We use this filtration\nto give some purely representation-theoretic conditions which are equivalent to\nthe existence of a Frobenius splitting of the double flag variety G/B \×\nG/B that maximally compatibly splits the diagonal. In particular, this gives a\nsufficient condition for Wahl's conjecture to hold for G and we use this\ncriterion to prove that Wahl's conjecture holds in type G2 for p at least 11.\n