Standard monomial theory for flag algebras of GL\((n)\)and Sp\((2n)\)

DOI10.1016/j.jalgebra.2008.02.025zbMath1152.13020OpenAlexW1964349414MaRDI QIDQ947483

Sangjib Kim

Publication date: 6 October 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.02.025

zbMATH Keywords

classical groupsYoung tableauxtoric degenerationsCombinatorial representation theoryflat algebras

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items

Pieri algebras for the orthogonal and symplectic groups, Standard bases for tensor products of exterior powers, Sign Hibi cones and the anti-row iterated Pieri algebras for the general linear groups, Distributive lattices, affine semigroups, and branching rules of the classical groups, Quivers, invariants and quotient correspondence, The nullcone in the multi-vector representation of the symplectic group and related combinatorics, Why should the Littlewood–Richardson Rule be true?, A basis for the symplectic group branching algebra, Hibi algebras and representation theory, Standard monomial bases and degenerations of \(SO_m(\mathbb C)\) representations, Toric degeneration of branching algebras

Cites Work

• SAGBI bases and degeneration of spherical varieties to toric varieties
• Young diagrams and determinantal varieties
• Representation-functors and flag-algebras for the classical groups. I
• Young tableaux, Gelfand patterns, and branching rules for classical groups
• Degenerations of flag and Schubert varieties to toric varieties
• Toric degenerations of Schubert varieties
• Toric degeneration of Schubert varieties and Gelfand--Tsetlin polytopes
• Representation functors and flag-algebras for the classical groups. II
• Weyl chambers and standard monomial theory for poset lattice cones
• Construction of Sp-modules by tableaux
• Geometry of 𝐺/𝑃
• Sagbi bases with applications to blow-up algebras.
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