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Showing 1 to 12 of 12 for “"flag variety"”.
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Rigid Analytic Quantum Groups
… and Kremnizer's construction of the quantum flag variety of a semisimple algebraic group, using a Banach completion of $\wideparen{\mathcal{O}_q(G)}$. Our main result is a Beilinson-Bernstein localisation theorem in this context. We define a category of $\lambda$-twisted $D$-modules on this …
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Lie Algebras of Differential Operators and D-modules
… of the diagonal in the square of the flag variety. Namely, we consider the Beilinson-Bernstein localization of the semiregular module and show that it is isomorphic to the D-module obtained by applying the Emerton-Nadler-Vilonen geometric Jacquet functor to the D-module of …
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Tilting sheaves for real groups and Koszul duality
… real form of an algebraic group acting on the flag variety we construct an analog of a Soergel functor, which fully-faithfully embeds the subcategory of tilting objects to the category of coherent sheaves on a block variety. We apply the results to give a new, purely geometric, proof of the …
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Affine Springer Fibers and the Kazhdan-Lusztig Map
… relating singular supports of IC sheaves on the flag variety with special nilpotent orbits. The second is a resolution of Lusztig’s conjecture that strata can be described by fibers of (parahoric) Kazhdan-Lusztig maps.
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The Frobenius direct image of line bundles and the structure of representations
… line bundles, ${\cal L}$($\lambda$), on the flag variety G/B, are important objects of study. E.g., their global sections form representations of G which are dual to the Weyl modules. In this thesis, our central object of study is the direct image of the induced line bundles under the …
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Combinatorics in Schubert varieties and Specht modules
… thesis, we link Schubert varieties in the full flag variety with hyperplane arrangements. Schubert varieties are parameterized by elements of the Weyl group. For each element of the Weyl group, we construct certain hyperplane arrangement. We show that the generating function for regions of this …
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Double affine galleries
… of this functor recovers the double affine flag variety at the level of sets, but we do not think that the colimit of schemes is well-behaved. Instead, we describe a different way of equipping the colimit set with a ringed space structure, and we conjecture that this ringed space is a …
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Prism tableaux and alternating sign matrices
… to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w in Fl(C^n). Schubert polynomials are indexed by elements of the symmetric group and form a basis of the ring Z[x1,x2,...]. The expansion of the …
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Kazhdan-Laumon Categories and Representations
… on the basic affine space and the semi-infinite flag variety. We then study the braid group action on D superscript b (G/U) (the main ingredient in Kazhdan and Laumon’s construction) and show that it categorifies the algebra of braids and ties, an algebra previously studied in knot theory; we …
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Kazhdan-Lusztig-Basen, unzerlegbare Bimoduln und die Topologie der Fahnenmannigfaltigkeit einer Kac-Moody-Gruppe
Wir betrachten graduierte Bimoduln über der symmetrischen Algebra S des <br>Dualraums der Cartanschen Unteralgebra einer Kac-Moody-Algebra, spezieller <br>diejenigen, die man als direkte Summanden iterierter Tensorprodukte von S <br>über den Invarianten (in S) von einfachen Spiegelungen erhält. …
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Root-theoretic Young diagrams and Schubert Calculus
… rules for the Schubert calculus of generalized flag varieties; that is, for the structure constants of their cohomology rings with respect to the Schubert basis. There are several natural choices of combinatorial indexing sets for the Schubert basis classes. This thesis examines a number of …
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On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution
We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. …