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

zbMATH Keywords

normality\(K\)-theorystandard monomial theorysemi-infinite flag manifoldsemi-infinite Lakshmibai-Seshadri pathPieri-Chevalley formula

Mathematics Subject Classification ID

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)

Related Items

Chevalley formula for anti-dominant minuscule fundamental weights in the equivariant quantum \(K\)-group of partial flag manifolds ⋮ Inverse \(K\)-Chevalley formulas for semi-infinite flag manifolds. II: Arbitrary weights in ADE type ⋮ Vertex algebras and coordinate rings of semi-infinite flags ⋮ New structure on the quantum alcove model with applications to representation theory and Schubert calculus ⋮ A combinatorial Chevalley formula for semi-infinite flag manifolds and its applications ⋮ The formal model of semi-infinite flag manifolds ⋮ Identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules over quantum affine algebras of type \(C\) ⋮ Generalized quantum Yang-Baxter moves and their application to Schubert calculus ⋮ Reduced arc schemes for Veronese embeddings and global Demazure modules ⋮ Tensor product decomposition theorem for quantum Lakshmibai-Seshadri paths and standard monomial theory for semi-infinite Lakshmibai-Seshadri paths ⋮ Chevalley formula for anti-dominant weights in the equivariant \(K\)-theory of semi-infinite flag manifolds ⋮ Beilinson–Drinfeld Schubert varieties and global Demazure modules ⋮ Frobenius splitting of Schubert varieties of semi-infinite flag manifolds ⋮ InverseK-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type ⋮ Tableau models for semi-infinite Bruhat order and level-zero representations of quantum affine algebras

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