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## Springer fiber components in the two columns case for types A and D are normal

Bulletin de la Societe Mathematique de France. 2012. Vol. 140. No. 3. P. 309-333.

Smirnov E., Perrin N.

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen-Macaulay, and have rational singularities.

Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...

Added: October 9, 2012

Michael Finkelberg, Andrei Ionov, Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2018 Vol. 13 No. 1 P. 31-42

We propose an r-variable version of Kostka-Shoji polynomials K_{λμ} for r-multipartitions λ, μ. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of a line bundle over Lusztig’s iterated convolution diagram for the cyclic quiver Ã_{r−1}. ...

Added: March 1, 2018

Feigin E., Cerulli Irelli G., Reineke M., Algebra & Number Theory 2012 Vol. 6 No. 1 P. 165-194

Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerate flag varieties investigated earlier by the second named author. This leads to the consideration of a class of Grassmannians of subrepresentations of the direct sum of a projective and ...

Added: June 29, 2012

Feigin E., Finkelberg M. V., Mathematische Zeitschrift 2013 Vol. 275 No. 1-2 P. 55-77

Let $Fl^a_\lambda$ be the PBW degeneration of the flag varieties of type $A_{n-1}$. These varieties are singular and are acted upon with the degenerate Lie group $SL_n^a$. We prove that $Fl^a_\lambda$ have rational singularities, are normal and locally complete intersections, and construct a desingularization $R_\lambda$ of $Fl^a_\lambda$. The varieties $R_\lambda$ can be viewed as towers ...

Added: September 18, 2013

Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 2 P. 337-361

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand-Tsetlin subalgebra of U(gln), and formulate a conjectural answer for the small quantum cohomology rings in terms of ...

Added: October 9, 2012

Feigin E., Selecta Mathematica, New Series 2012 Vol. 18 No. 3 P. 513-537

Let Fλ be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module Vλ. We define a flat degeneration Fλa, which is a GaM variety. Moreover, there exists a larger group Ga acting on Fλa, which is a degeneration of the group G. The group Ga contains ...

Added: August 31, 2012

Esterov A. I., Discrete and Computational Geometry 2010 Vol. 44 No. 1 P. 96-148

For a system of polynomial equations, whose coefficients depend on parameters, the Newton polyhedron of its discriminant is computed in terms of the Newton polyhedra of the coefficients. This leads to an explicit formula (involving mixed fiber polyhedra and Euler obstructions of toric varieties) in the unmixed case, suggests certain open questions in general, and ...

Added: December 10, 2012

Kaledin D., Moscow Mathematical Journal 2012 Vol. 12 No. 3 P. 593-604

We give a direct interpretation of the Witt vector product in terms of tame residue in algebraic K-theory. ...

Added: October 25, 2012

Cerulli Irelli G., Feigin E., Reineke M., Degenerate flag varieties: moment graphs and Schroeder numbers / Cornell University. Series math "arxiv.org". 2012. No. 1206.4178.

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study ...

Added: June 29, 2012

Feigin M., Shramov K., International Mathematics Research Notes 2012 Vol. 2012 No. 15 P. 3375-3414

We consider representations of rational Cherednik algebras that are particular ideals in the ring of polynomials. We investigate convergence of the integrals that express the Gaussian inner product on these representations. We derive that the integrals converge for the minimal submodules in types B and D for the singular values suggested by Cherednik with at ...

Added: September 13, 2012

I.I. Bogdanov, Kuyumzhiyan K., Mathematical notes 2012 Vol. 92 No. 3-4 P. 445-457

Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following property: for every vector v ∈ V, the closure of its T-orbit is a normal affine variety. To solve this problem, ...

Added: February 4, 2013

Chari V., Loktev S., Journal of Algebra 2012 Vol. 349 No. 1 P. 317-328

We identify the sl(n+1) isotypical components of the global Weyl modules W(kω1) with certain natural subspaces of the polynomial ring in k variables. We then apply the representation theory of current algebras to classical problems in invariant theory. ...

Added: September 29, 2012

Kiritchenko V., Timorin V., Smirnov E., Oberwolfach Reports 2011 Vol. 8 No. 3 P. 2341-2344

We construct generalized Newton polytopes for Schubert subvarieties in the variety of complete flags in C^n . Every such “polytope” is a union of faces of a Gelfand–Zetlin polytope (the latter is a well-known Newton–Okounkov body for the flag variety). These unions of faces are responsible for Demazure characters of Schubert varieties and were originally used ...

Added: November 17, 2012

Prokhorov Y., Journal of Algebraic Geometry 2012 Vol. 21 No. 3 P. 563-600

We classify all finite simple subgroups of the Cremona group Cr3(C). ...

Added: September 19, 2012

Providence: American Mathematical Society, 2012

The volume is to contain the proceedings of the 13th conference AGCT as well as the proceedings of the conference Geocrypt. The conferences focus on various aspects of arithmetic and algebraic geometry, number theory, coding theory and cryptography. The main topics discussed at conferences include the theory of curves over finite fields, theory of abelian ...

Added: January 3, 2013

Oberwolfach: European Mathematical Society Publishing house, 2012

В сборнике печатаются труды конференций Математического Института Обервольфаха. ...

Added: November 17, 2012

M.: Higher School of Economics Publishing House, 2012

Toric geometry exhibited a profound relation between algebra and topology on one side and combinatorics and convex geometry on the other side. In the last decades, the interplay between algebraic and convex geometry has been explored and used successfully in a much more general setting: first, for varieties with an algebraic group action (such as ...

Added: November 17, 2012

Benett M., Berenstein A., Chari V. et al., Selecta Mathematica, New Series 2014 No. 2 P. 585-607

We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category O of modules for g and in this paper, we use the combinatorics of Macdonald polynomials to prove an analogue of the famous BGG duality in ...

Added: September 29, 2012

Shirokov D., Николай Гурьевич Марчук, Красанд/URSS, 2020

The book deals with several actual branches of Clifford algebra theory. Clifford algebras are used in mathematics, physics, mechanics, engineering, signal processing, etc. We discuss in details a representation theory of Clifford algebras. Also we discuss the connection between spin and orthogonal groups, Pauli theorem. We develop a method of quaternion typification of Clifford algebra ...

Added: December 11, 2020

Andrey Soldatenkov, International Mathematics Research Notices 2012 Vol. 2012 No. 15 P. 3483-3497

A hypercomplex structure on a smooth manifold is a triple of integrable almost complex structures satisfying quaternionic relations. The Obata connection is the unique torsion-free connection that preserves each of the complex structures. The holonomy group of the Obata connection is contained in GL(n, H). There is a well-known construction of hypercomplex structures on Lie ...

Added: January 17, 2013

Trubochkina N. K., Качество. Инновации. Образование 2012 Т. 84 № 5 С. 76-82

Scientific and exploratory research and mathematical simulation of a fractal designresults are presented. Decorative fractal patterns for textile and construction industries (models, murals, stained glass) have been developed. Fractals, which can be attributed to a class of fractal artdeveloped. Technology of frost-and water-resistant seamless large area fractal frescoes developed. Technology cost much less than for ...

Added: November 21, 2012

Feigin B. L., Buryak A., Journal of Geometry and Physics 2012 Vol. 62 No. 7 P. 1652-1664

The moduli space M(r,n) of framed torsion free sheaves on the projective plane with rank r and second Chern class equal to n has the natural action of the (r+2)-dimensional torus. In this paper, we look at the fixed point set of different one-dimensional subtori in this torus. We prove that in the homogeneous case ...

Added: September 20, 2012

Zykin A. I., Lebacque P. undefined., Publications Mathematiques de Besancon 2011 P. 47-73

The paper is a survey of recent developments in the asymptotic theory of global fields and varieties over them. First, we give a detailed motivated introduction to the asymptotic theory of global fields which is already well shaped as a subject. Second, we treat in a more sketchy way the higher dimensional theory where much ...

Added: January 3, 2013

Popov V., Problems for the problem session / Centro Internazionale per la Ricerca Matematica. Series CIRM "Electronic preprint server". 2012. No. нет.

Some problems on the structure of the Cremona groups formulated (with comments) by the author at the International conference Birational and Affine Geometry, Levico Terme (Trento), 29.10.12--03.11.12 ...

Added: January 9, 2013