Geometry of G/P. VI: Bases for fundamental represenations of classical groups. Geometry of G/P. VII: The symplectic group and the involution \(\sigma\) . Geometry of G/P. VIII: The group \(SO(2n+1)\) and the involution \(\sigma\)

DOI10.1016/0021-8693(87)90108-6zbMath0618.14027OpenAlexW2079842866MaRDI QIDQ1089060

Venkatramani Lakshmibai

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90108-6

zbMATH Keywords

standard monomial theorymaximal parabolic subgroupsingular loci of the Schubert varieties

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (9)

Geometry of G/P. VI: Bases for fundamental represenations of classical groups. Geometry of G/P. VII: The symplectic group and the involution \(\sigma\) . Geometry of G/P. VIII: The group \(SO(2n+1)\) and the involution \(\sigma\) ⋮ A criterion for smoothness of Schubert varieties in \(Sp(2n)/B\) ⋮ Geometry of \(G/P\). IX: The group \(SO(2n)\) and the involution \(\sigma\) ⋮ On tangent spaces to Schubert varieties. II ⋮ Standard monomial theoretic proof of prv conjecture ⋮ Frobenius splittings and blow-ups ⋮ On tangent spaces to Schubert varieties ⋮ On Zariski tangent spaces of Schubert varieties, and a proof of a conjecture of Deodhar ⋮ Multiplicities of points on a Schubert variety in a minuscule G/P

Cites Work

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• Geometry of G/P. V
• Geometry of G/P. VI: Bases for fundamental represenations of classical groups. Geometry of G/P. VII: The symplectic group and the involution \(\sigma\) . Geometry of G/P. VIII: The group \(SO(2n+1)\) and the involution \(\sigma\)
• Classical Bruhat orders and lexicographic shellability
• Lectures on Chevalley Groups
• Singular locus of a Schubert variety
• Singular loci of Schubert varieties for classical groups
• Geometry of G/P-II [The work of De Concini and Procesi and the basic conjectures]
• Geometry of 𝐺/𝑃
• Arithmetic Cohen-Macaulayness and Arithmetic Normality for Schubert Varieties

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