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Showing 1 to 8 of 8 for “"affine Grassmannian"”.
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Matrix Schubert varieties for the affine Grassmannian
… the Borel-Moore homology of the (special linear) affine Grassmannian by an analogous process. This requires finitizing an affine Schubert variety to produce a matrix affine Schubert variety. This involves a choice of ``window'', so one must then identify a class representative that is independent …
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The Beilinson-Bernstein localization theorem for the affine Grassmannian
… of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.
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Equivariant quantum cohomology and the geometric Satake equivalence
… new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a …
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Some results related to the quantum geometric Langlands program
… category of spherical perverse sheaves on the affine Grassmannian of a reductive group G and the category of representations of its Langlands dual group. The category of spherical perverse sheaves sits naturally in an equivariant derived category, and this larger category was described in terms …
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Diagrams of affine permutations and their labellings
We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by Fomin- Greene-Reiner-Shimozono, and we extend this notion to affine permutations. The balanced labellings give a natural encoding of the …
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Dual Filtered Graphs for Kac-Moody algebras
… the dual multiplication map of K-cohomology of affine Grassmannian $Gr_G$. We conjecture that the strong filtered graph and weak filtered graph are dual, which means we get an identity when we apply the up and down operators on the vertices. We proved this identity except one case that where we …
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Data Association Algorithms and Representations for Robust Geometric Perception
… representation for lines and planes using the affine Grassmannian manifold. This thesis looks beyond points to higherorder geometric abstractions and provides a means for robustly aligning line and plane landmarks without an initial guess. When applied to lidar-based localization and loop …
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A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group
For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and …