Their flag varieties and representation theory

By Shrawan Kumar, Kac-moody Groups. 2002

110 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7328398477204f9d013af2d6fa3a5c1098eee437

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

K-theory Schubert calculus of the affine Grassmannian (2009, unknown): “In contrast to [KK90] which uses the “thin” Kac-Moody flag manifold Xind which is an indscheme with finite-dimensional Schubert varieties [Kum], we employ the larger “thick” KacMoody flag manifold X [Kas], which is a scheme of infinite type with finite codimensional Schubert varieties.”
Back stable Schubert calculus (2018, background): “Nevertheless, F̃l · n is known to be an ind-variety over C [Kum].”
On the shape of Bruhat intervals (2005, background): “General referen es for ba kground to this material are the books by Ka [Ka 83℄ and Kumar [Ku02℄, for the algebrai -geometri aspe ts see [Ku02℄ and [Sl86℄.”
On the coherence conjecture of Pappas and Rapoport (2010, background): “When G is an almost simple, simply-connected algebraic group over k((t)) and G is a parahoric group scheme of G, F`G is ind-projective and coincides with the affine flag varieties arising from the theory of affine Kac-Moody groups as developed in [Kum02], [Mat88] (at least when G splits over a tamel”
On the geometry of the automorphism groups of affine varieties (2018, background): “Kumar’s book [Kum02] contains in Section IV an introduction to ind-varieties and ind-groups, with complete and detailed proofs, and with [Sha81] as a basic reference.”
Parity Sheaves (2009, background): “The standard reference for Kac-Moody Schubert varieties is [Kum02].”
Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties (2010, methodology): “For a detailed construction of these varieties in the Kac-Moody setting the reader is referred to [Kum02].”