Richardson varieties and equivariant \(K\)-theory.

DOI10.1016/S0021-8693(02)00634-8zbMath1071.14049arXivmath/0201075MaRDI QIDQ1868752

Venkatramani Lakshmibai, Peter Littelmann

Publication date: 28 April 2003

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

Full work available at URL: https://arxiv.org/abs/math/0201075

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Equivariant (K)-theory (19L47) Classical problems, Schubert calculus (14N15)

Related Items

Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian ⋮ Quantum analogues of Richardson varieties in the Grassmannian and their toric degeneration. ⋮ Standard monomial theory for desingularized Richardson varieties in the flag variety \(\mathrm{GL}(n)/B\) ⋮ Dimers, webs, and positroids ⋮ Projective normality of torus quotients of flag varieties ⋮ Cyclic Demazure modules and positroid varieties ⋮ Torus quotient of Richardson varieties in orthogonal and symplectic grassmannians ⋮ Geometry of pure spinor formalism in superstring theory ⋮ Torus quotients of Richardson varieties ⋮ On the \(T\)-leaves of some Poisson structures related to products of flag varieties ⋮ Standard monomial theory and toric degenerations of Richardson varieties in flag varieties ⋮ Multiplicity on a Richardson variety in a cominuscule $G/P$ ⋮ Frobenius splitting of Schubert varieties of semi-infinite flag manifolds

Cites Work

• A plactic algebra for semisimple Lie algebras
• Schubert varieties are arithmetically Cohen-Macaulay
• Projective normality of flag varieties and Schubert varieties
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Geometry of G/P. V
• Representations of Coxeter groups and Hecke algebras
• Intersections of double cosets in algebraic groups
• A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras
• Frobenius splitting in characteristic zero and the quantum Frobenius map
• Positivity of some intersections in \(K_0(G/B)\)
• LS algebras and application to Schubert varieties
• Algebraization of Frobenius splitting via quantum groups.
• A Pieri formula in the Grothendieck ring of a flag bundle
• Positivity in the Grothendieck group of complex flag varieties.
• Parabolic subgroups with Abelian unipotent radical
• T -equivariant K -theory of generalized flag varieties
• Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras
• A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item