Flag varieties. An interplay of geometry, combinatorics, and representation theory

DOI10.1007/978-93-86279-41-5zbMath1166.14001OpenAlexW4240774482MaRDI QIDQ5901524

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Publication date: 8 April 2009

Published in: Texts and Readings in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-93-86279-41-5

zbMATH Keywords

toric varietySchubert varietycharacterLie algebratableauxsymmetric groupflag varietystandard monomial theoryinvariant theorygeneral linear groupSchur-Weyl dualitysingular locusChevalley groupfinite groupalgebraic groupsheaf cohomologyalgebraic geometryspecial linear groupcommutative algebrairreducible moduleBorel subgroupdeterminantal varietyparabolic subgroupBruhat decompositionGrassmannian varietysemisimple ring

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Linear algebraic groups over arbitrary fields (20G15) Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry (14-01) Lie algebras and Lie superalgebras (17Bxx) Algebraic groups (14Lxx) Special varieties (14Mxx) General commutative ring theory (13Axx)

Related Items (10)

A direct way to find the right key of a semistandard Young tableau ⋮ Projective normality of torus quotients of flag varieties ⋮ Torus quotient of the Grassmannian \(G_{n,2n}\) ⋮ Torus quotients of Richardson varieties in \(G_{r, qr+1}\) ⋮ Structural matrix algebras, generalized flags, and gradings ⋮ Semistandard tableaux for Demazure characters (key polynomials) and their atoms ⋮ Association schemes on the Schubert cells of a Grassmannian ⋮ The Heisenberg product seen as a branching problem for connected reductive groups, stability properties ⋮ On the regularity of join-meet ideals of modular lattices ⋮ Accessible proof of standard monomial basis for coordinatization of Schubert sets of flags

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