2024 Cohomology of flag variety

Cohomology of flag variety

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WebApr 10, 2024 · Related News. 0 Perverse sheaves on affine flag varieties and coherent sheaves on the dual Steinberg variety. Abstract: We will report on an ongoing project with R. Bezrukavnikov and L. Rider which aims at constructing an equivalence of categories lifting to the categorical level the comparison between the two natural geometric … WebThe identification of the cohomology ring with the coinvariant algebra of the Weyl group has continued to be important for algebraic and geometric questions, for instance in the work of Beilinson-Ginzburg-Soergel. While Hiller's notes are not entirely self-contained, they are …

Hecke algebra and equivariant cohomology of flag varieties

WebB. Kostant and S. Kumar: The nil Hecke ring and cohomology of G/P for a Kac-Moody group G, Adv. Math. 62 (1986), 187–237. CrossRef Google Scholar B. Kostant and S. Kumar: T-equivariant K-theory of generalized … WebTour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site ravi doshi

Hecke algebra and equivariant cohomology of flag varieties

WebJun 21, 2024 · PBW degenerations are a particularly nice family of flat degenerations of type A flag varieties. We show that the cohomology of any PBW degeneration of the flag variety surjects onto the cohomology of the original flag variety, and that this holds in an equivariant setting too. We also prove that the same is true in the symplectic setting … WebAug 11, 2009 · We show that many of the structure constants of the quantum cohomology of flag varieties can be computed from the image of the evaluation morphism. In fact, we show that a certain class of these structure constants are equal to the ordinary intersection of Schubert cycles in a related flag variety. druk ceidg-1 biznes gov

Reference for Hodge decomposition for flag variety

Webtion of equivariant cohomology ring of a ne ag varieties and suggest an attempt, with partial results on sl(2), to compute the equivariant cohomology of a ne Springer bers under the GKM description. 1 Introduction and Preliminaries For any topological spase, there exists the notion of cohomology which embraces topologi-cal properties algebraically. Web2/6 Cohomology of global Shimura varieties and the global correspondence [speaker: Alex Bauman] 2/13 Integral models of Shimura varieties [speaker: ... Abstract: The Borel-Weil-Bott theorem describes the cohomology of line bundles on flag varieties as certain representations. In particular, the Borel-Weil-Bott theorem gives a geometric ... druk cfr-1WebSep 24, 2014 · Equivariant oriented cohomology of flag varieties @article{Calms2014EquivariantOC, title={Equivariant oriented cohomology of flag varieties}, author={Baptiste Calm{\`e}s and Kirill Zainoulline and Changlong Zhong}, journal={arXiv: Algebraic Geometry}, year={2014} } B. Calmès, K. Zainoulline, Changlong … ravi dox

"WebThe emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g. " - Cohomology of flag variety

Cohomology of flag variety

Equivariant oriented cohomology of flag varieties

WebWe establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the pres… WebCLASSICAL ASPECTS OF QUANTUM COHOMOLOGY OF FLAG VARIETIES 3 Theorem1.2. Let u,v,w∈ Sn+1 and λ∈ Q∨.If uis of Grassmannian type, then there exist v ′,w ∈ Sn+1 such that Nw,λ u,v = N w ...

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WebTHE NULL-CONE AND COHOMOLOGY OF VECTOR BUNDLES ON FLAG VARIETIES KARI VILONEN AND TING XUE Abstract. We study the null-cone of a semi-simple algebraic group acting on ... Let us consider the ﬂag variety X = G/B, where we think of having … http://www-personal.umich.edu/~charchan/seminar/

WebJun 8, 2015 · We show that the cohomology of the affine flag variety is product of the cohomology of an affine Grassmannian and a flag variety, which are generated by MN elements and Dunkl elements respectively. The Schubert classes in cohomology of the affine Grassmannian (resp. the flag variety) can be identified with affine Schur functions … WebCOHOMOLOGY OF THE FLAG VARIETIES TAO GUI Abstract. We study the Sn-equivariant log-concavity of the cohomology of ﬂag varieties, also known as the coinvariant ring of Sn. Using the theory of representation stability, we give computer …

WebThe sheaf cohomology groups of G-equivariant bundles on ﬂag varieties of G(often called homogeneous bundles) are G-representations, and a central question is to deter- mine which G-representations appear in the cohomology of these bundles. WebSep 1, 2024 · Lanini and Strickland also study the cohomology of PBW degenerated flag varieties in [LS19]. One of the achievements of this framework is finding new monomial bases for gr V (λ), and hence for V ...

WebMar 24, 2008 · Cohomology of Flag Varieties and the Brylinski-Kostant Filtration Chuck Hague Let G be a semisimple complex algebraic group with Borel subgroup B and let P be a parabolic subgroup of G.

Webag variety for SL 3 and the Grassmanian Grp2;4q. A more complete description and combinatorial model of the equivariant cohomology of ... The cohomology of the complex of K-equivariant cochains is isomorphic to equivariant cohomology de ned above. Example 2. Let T S1. Then, the equivariant chains in H pptqare given by compact spaces Cwith a ... ravi dosa cp tankWebJan 19, 2015 · There are quantum, noncommutative and infinite-dimensional generalizations. Flag varieties have rich combinatorial and geometric structure and play an important role in representation theory and integrable systems. Related concepts. … drukčijiWebThe algebraic/combinatorial method in the study of cohomology of flag varieties was started by Demazure and Bernstein-Gelfand-Gelfand in 1970s (for ordinary Chow groups), and were continued by Arabia, Kostant-Kumar, Bressler-Evens in 1980s-1990s (for equivariant singular cohomology, equivariant K-theory and complex cobordism). ravidoxu-suWebSep 6, 2024 · Quiver flag varieties are generalisations of type A flag varieties; this result is new even in the flag case. This gives an effective way of computing products in their cohomology, reducing computations to that in the cohomology ring of the Grassmannian. We then prove a quantum rim-hook rule for Fano quiver flag varieties (including type A … drukciji.baWebB. Kostant and S. Kumar: The nil Hecke ring and cohomology of G/P for a Kac-Moody group G, Adv. Math. 62 (1986), 187–237. CrossRef Google Scholar B. Kostant and S. Kumar: T-equivariant K-theory of generalized flag varieties, J. Differential Geom. 32 … drukciji baWebSome facts on cohomology We ﬂrst state some properties of cohomology which will be used in what follows. LetYbe a nonsingular projective variety. We then have the following: (1) An irreducible subvarietyZof codimensiondinYdetermines a cohomology class [Z]2 H2d(Y). (2) IfYhas dimensionN, thenH2N(Y) = Z, with the class of a point being a generator. ravi double glazingWebNov 18, 2024 · Cohomology of line bundles on flag varieties in positive characteristic. Let G be a semi-simple algebraic group over an algebraically closed field k of positive characteristic and let B be a Borel subgroup. The cohomology of line bundles on the … drukčiji ba