Levi subgroup actions on Schubert varieties, induced decompositions of their coordinate rings, and sphericity consequences

DOI10.1007/s10468-017-9744-6OpenAlexW2964024269MaRDI QIDQ1737205

Venkatramani Lakshmibai, Reuven Hodges

Publication date: 27 March 2019

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.09538

zbMATH Keywords

algebraic groupsSchubert varietiesrepresentation theorycoordinate ringsspherical varietiesLevi subgroup

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Representations of finite groups of Lie type (20C33) Compactifications; symmetric and spherical varieties (14M27)

Related Items (5)

Levi-spherical Schubert varieties ⋮ Toroidal Schubert varieties ⋮ Multiplicity-free skew Schur polynomials ⋮ Coxeter combinatorics and spherical Schubert geometry ⋮ A classification of spherical Schubert varieties in the Grassmannian

Cites Work

• Homogeneous spaces and equivariant embeddings
• Introduction to the theory of standard monomials. With notes by Peter Littelmann and Pradeep Shukla. Appendix by V. Lakshmibai
• Polynomial representations of \(\text{GL}_n\). With an appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J. A. Green and M. Schocker.
• Espaces homogènes sphériques. (Spherical homogeneous spaces)
• The Grassmannian variety. Geometric and representation-theoretic aspects
• Standard monomial theory. Invariant theoretic approach
• Stable branching rules for classical symmetric pairs
• Cohomology of line bundles on $G/B$
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