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Of all publications in the section: 6
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Article
Losev Ivan. International Mathematical Research Notices. 2015. No. 18. P. 8860-8873.

In this paper we prove the abelian localization theorem for modules over cyclotomic Rational Cherednik algebras.

Added: Oct 15, 2017
Article
Buryak A., Feigin B. L., Nakajima H. International Mathematical Research Notices. 2015. Vol. 2015. No. 13. P. 4708-4715.

In a recent paper the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper we give a very short geometrical proof of that formula.

Added: Sep 29, 2020
Article
Rogov V. International Mathematical Research Notices. 2018. P. 1-20.

An Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient G/, where G is the group of complex unipotent 3 × 3 matrices and  ⊂ G is a cocompact lattice. In this work, we study holomorphic submanifolds in Iwasawa manifolds. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic subtorus. We also prove that any complex surface in an Iwasawa manifold is either an abelian surface or a Kähler non-projective isotrivial elliptic surface of Kodaira dimension one. In the Appendix, we show that any subtorus in Iwasawa manifold carries complex multiplication.

Added: Mar 18, 2019
Article
Brundan J., Losev Ivan, Webster B. International Mathematical Research Notices. 2017. No. 20. P. 6329-6410.

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie super algebra gl_{n|m}(C) as formulated originally by the first author. We also prove for the first time that any integral block of category O for gl_{n|m}(C) (and also all of its parabolic analogs) possesses a graded version which is Koszul. Our approach depends crucially on an application of the uniqueness of tensor product categorifications established recently by the second two authors.

Added: Oct 15, 2017
Article
Ayzenberg A., Buchstaber V. International Mathematical Research Notices. 2020. Vol. 388. P. 1-12.

We consider the space $X_h$ of Hermitian matrices having staircase form and the given simple spectrum. There is a natural action of a compact torus on this space. Using generalized Toda flow, we show that $X_h$ is a smooth manifold and its smooth type is independent of the spectrum. Morse theory is then used to show the vanishing of odd degree cohomology, so that $X_h$ is an equivariantly formal manifold. The equivariant and ordinary cohomology rings of $X_h$ are described using GKM-theory. The main goal of this paper is to show the connection between the manifolds $X_h$ and regular semisimple Hessenberg varieties well known in algebraic geometry. Both spaces $X_h$ and Hessenberg varieties form wonderful families of submanifolds in the complete flag variety. There is a certain symmetry between these families which can be generalized to other submanifolds of the flag variety.

Added: Jan 14, 2020
Article
Feigin E., Makedonskyi I. International Mathematical Research Notices. 2020. No. 14. P. 4357-4394.

The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

Added: Sep 1, 2020