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On Lagrangian spheres in the flag variety F 3
Mathematical notes. 2015. Vol. 98. No. 1-2. P. 348–351.
Tyurin N. A.
Publication based on the results of:
Bochkarev M., Ignatyev M. V., Shevchenko A. A., Journal of Algebra 2016 Vol. 465 No. November P. 259–286
We study tangent cones to Schubert subvarieties of the flag variety of a complex reductive group G. Let T be a maximal torus of G, B be a Borel subgroup of G containing T, Φ be the root system of G with respect to T, W be the Weyl group of Φ, and F=G/B be ...
Added: October 8, 2016
Feigin B. L., Makhlin I., / Series math "arxiv.org". 2015.
We present a new combinatorial formula for Hall-Littlewood functions associated with the affine root system of type A~n−1, i.e. corresponding to the affine Lie algebra slˆn. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation.Our formula can ...
Added: August 7, 2015
Makhlin I., / Series math "arxiv.org". 2014.
We exploit the idea that the character of an irreducible finite dimensional gln-module is the sum of certain exponents of integer points in a Gelfand-Tsetlin polytope and can thus be calculated via Brion's theorem. In order to show how the result of such a calculation matches Weyl's character formula we prove some interesting combinatorial traits ...
Added: August 7, 2015
Olshanski G., Journal of Lie Theory 2013 Vol. 23 No. 4 P. 1011–1022
The unitary group U(N) acts by conjugations on the space H(N) of NxN Hermitian matrices, and every orbit of this action carries a unique invariant probability measure called an orbital measure. Consider the projection of the space H(N) onto the real line assigning to an Hermitian matrix its (1,1)-entry. Under this projection, the density of ...
Added: November 24, 2013
Kiritchenko V., Smirnov E., Timorin V., Russian Mathematical Surveys 2012 Vol. 67 No. 4 P. 685–719
A new approach is described to the Schubert calculus on complete flag varieties, using the volume polynomial associated with Gelfand- Zetlin polytopes. This approach makes it possible to compute the intersection products of Schubert cycles by intersecting faces of a polytope. Bibliography: 23 titles. ...
Added: February 4, 2013
Kiritchenko V., Smirnov E., Timorin V., Успехи математических наук 2012 Т. 67 № 4 С. 89–128
We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope. ...
Added: September 19, 2012