Projected Richardson varieties and affine Schubert varieties
Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2385-2412.

Let G be a complex quasi-simple algebraic group and G/P be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of G/P. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of G. Furthermore, we compare the torus-equivariant cohomology and K-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type A.

Soit G un groupe algébrique complexe quasi-simple et G/P une variété de drapeaux partiels. La projection sur G/P des variétés de Richardson (de la variété des drapeaux complets) forment une stratification de G/P. Nous montrons que les relations d’adhérence des variétés de Richardson projetées correspondent à celles d’un certain sous-ensemble de variétés de Schubert sur la variété de drapeaux affine de G. Nous comparons aussi les classes de cohomologie équivariante et de K-théorie de ces deux stratifications. Notre travail généralise celui de Knutson, Lam et Speyer pour la grassmannienne de type A.

DOI: 10.5802/aif.2990
Classification: 14M15,  05E10
Keywords: flag variety, Schubert calculus, projected Richardson variety, affine Schubert variety
He, Xuhua 1; Lam, Thomas 2

1 Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon, Hong Kong (China)
2 Department of Mathematics University of Michigan Ann Arbor MI 48109 (USA)
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He, Xuhua; Lam, Thomas. Projected Richardson varieties and affine Schubert varieties. Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2385-2412. doi : 10.5802/aif.2990. http://archive.numdam.org/articles/10.5802/aif.2990/

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