Lectures on Frobenius splittings and \(B\)-modules

zbMath0815.20027MaRDI QIDQ1316606

Wilberd van der Kallen

Publication date: 27 February 1994

Published in: Lectures on Mathematics and Physics. Mathematics. Tata Institute of Fundamental Research (Search for Journal in Brave)

zbMATH Keywords

Weyl groupSchubert varietiesflag varietyreductive groupsline bundledesingularizationtensor productdual Weyl modulesgood filtrationsvanishing theoremssemi-simple algebraic groupFrobenius splittingDemazure's character formuladual Joseph modulesexcellent filtrationrestriction to parabolic subgroupsSchubert filtrations

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Cohomology theory for linear algebraic groups (20G10) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (21)

Reductive embeddings are Cohen-Macaulay ⋮ The Cohen-Macaulay property of separating invariants of finite groups ⋮ Truncation and the induction theorem ⋮ Some good-filtration subgroups of simple algebraic groups. ⋮ On the collapsing of homogeneous bundles in arbitrary characteristic ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ First degree cohomology of Specht modules and extensions of symmetric powers ⋮ The space of triangles, vanishing theorems, and combinatorics ⋮ Computing invariants of algebraic groups in arbitrary characteristic ⋮ On the B-canonical splittings of flag varieties ⋮ Steinberg modules and Donkin pairs ⋮ Finite good filtration dimension for modules over an algebra with good filtration. ⋮ Finite Schur filtration dimension for modules over an algebra with Schur filtration. ⋮ An approach towards Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules ⋮ Refinements of the Littlewood-Richardson rule ⋮ Borel-Weil theorem for configuration varieties and Schur modules ⋮ On the combinatorics of \(B\times B\)-orbits on group compactifications ⋮ Modules with a Demazure flag ⋮ Wahl's conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians ⋮ Large Schubert varieties ⋮ Positivity of some intersections in \(K_0(G/B)\)

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