Positivity in the Grothendieck group of complex flag varieties.

DOI10.1016/S0021-8693(02)00505-7zbMath1052.14054arXivmath/0105254OpenAlexW1973458870MaRDI QIDQ1858273

Michel Brion

Publication date: 12 February 2003

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

Full work available at URL: https://arxiv.org/abs/math/0105254

zbMATH Keywords

Schubert calculus

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Grassmannians, Schubert varieties, flag manifolds (14M15) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Grothendieck groups, (K)-theory and commutative rings (13D15)

Related Items

Singularities of Generalized Richardson Varieties, Affine Hecke algebras and the Schubert calculus, Quiver coefficients of Dynkin type, Pieri rules for the K-theory of cominuscule Grassmannians, Standard monomial theory for desingularized Richardson varieties in the flag variety \(\mathrm{GL}(n)/B\), \(K\)-theoretic Pieri rule via iterated residues, \(K\)-theory of minuscule varieties, Genomic tableaux, Projected Gromov-Witten varieties in cominuscule spaces, Positivity and Kleiman transversality in equivariant \(K\)-theory of homogeneous spaces, Cohomological consequences of the pattern map, Frozen pipes: lattice models for Grothendieck polynomials, Combinatorial formulas for shifted dual stable Grothendieck polynomials, Top-degree components of Grothendieck and Lascoux polynomials, Quantum \(K\)-theory of incidence varieties, Schubert calculus and quiver varieties, Asymmetric Function Theory, Equivariant \(K\)-theory of semi-infinite flag manifolds and the Pieri-Chevalley formula, Polynomials for \(\mathrm{GL}_p\times \mathrm{GL}_q\) orbit closures in the flag variety, Oriented Schubert calculus in Chow–Witt rings of Grassmannians, Positivity in \(T\)-equivariant \(K\)-theory of flag varieties associated to Kac-Moody groups, The \(K\)-theory of the flag variety and the Fomin--Kirillov quadratic algebra, Equivariant \(K\)-theory of Bott towers. Application to the multiplicative structure of the equivariant \(K\)-theory of flag varieties, Unnamed Item, Structure constants for Chern classes of Schubert cells, Projected Richardson varieties and affine Schubert varieties, A Kleiman–Bertini theorem for sheaf tensor products, Equivariant Hirzebruch class for singular varieties, A matroid invariant via the \(K\)-theory of the Grassmannian, Multiplicity on a Richardson variety in a cominuscule $G/P$, A Pieri-type formula for the ${K}$-theory of a flag manifold, Grothendieck classes of quiver varieties., A Littlewood-Richardson rule for the \(K\)-theory of Grassmannians., Richardson varieties and equivariant \(K\)-theory.

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