Equivariant \(K\)-theory of semi-infinite flag manifolds and the Pieri-Chevalley formula
DOI10.1215/00127094-2020-0015zbMath1475.17024arXiv1702.02408OpenAlexW3046801362MaRDI QIDQ2217883
Satoshi Naito, Daisuke Sagaki, Syu Kato
Publication date: 12 January 2021
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.02408
normality\(K\)-theorystandard monomial theorysemi-infinite flag manifoldsemi-infinite Lakshmibai-Seshadri pathPieri-Chevalley formula
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Classical problems, Schubert calculus (14N15)
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Cites Work
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- Demazure submodules of level-zero extremal weight modules and specializations of Macdonald polynomials
- Positivity and Kleiman transversality in equivariant \(K\)-theory of homogeneous spaces
- Quantum cohomology of \(G/P\) and homology of affine Grassmannian
- Weyl modules, Demazure modules and finite crystals for non-simply laced type
- Crystal bases and two-sided cells of quantum affine algebras
- Affine Kac-Moody algebras and semi-infinite flag manifolds
- T-equivariant K-theory of generalized flag varieties
- Path model for a level-zero extremal weight module over a quantum affine algebra. II
- Modules over the small quantum group and semi-infinite flag manifold
- Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
- Semi-infinite Lakshmibai-Seshadri path model for level-zero extremal weight modules over quantum affine algebras
- Hecke algebras and Jantzen's generic decomposition patterns
- Finite-dimensional representations of quantum affine algebras
- Stable bundles, representation theory and Hermitian operators
- Crystal bases of modified quantized enveloping algebra
- Geometric Eisenstein series
- Quantum \(K\)-theory on flag manifolds, finite-difference Toda lattices and quantum groups
- Positivity of some intersections in \(K_0(G/B)\)
- Demazure character formula for semi-infinite flag varieties
- A conjectural Peterson isomorphism in \(K\)-theory
- On level-zero representation of quantized affine algebras.
- Kac-Moody groups, their flag varieties and representation theory
- Positivity in the Grothendieck group of complex flag varieties.
- Paths and root operators in representation theory
- Weyl modules and \(q\)-Whittaker functions
- Level zero fundamental representations over quantized affine algebras and Demazure modules
- The strong Macdonald conjecture and Hodge theory on the loop Grassmannian
- Rogers-Ramanujan type identities and nil-DAHA
- Semi-infinite Schubert varieties and quantum 𝐾-theory of flag manifolds
- Two-sided BGG resolutions of admissible representations
- Equivariant K-Chevalley rules for Kac-Moody flag manifolds
- Combinatorics of Coxeter Groups
- Schubert calculus and representations of the general linear group
- Specialization of nonsymmetric Macdonald polynomials at 𝑡=∞ and Demazure submodules of level-zero extremal weight modules
- A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle
- A Uniform Model for Kirillov–Reshetikhin Crystals II. Alcove Model, Path Model, and $P=X$
- Semiinfinite Flags. I. Case of global curve $P^1$
- Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces
- A Uniform Model for Kirillov-Reshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graph
- Positivity in 𝑇-equivariant 𝐾-theory of flag varieties associated to Kac-Moody groups II
- Twisted zastava and q-Whittaker functions
- Affine Weyl Groups in K-Theory and Representation Theory