# Stability inequalities and universal Schubert calculus of rank 2

@article{Berenstein2010StabilityIA,
title={Stability inequalities and universal Schubert calculus of rank 2},
journal={Transformation Groups},
year={2010},
volume={16},
pages={955-1007}
}
• Published 10 August 2010
• Mathematics
• Transformation Groups
The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each “sufficiently rich” spherical building Y of type W we associate a certain cohomology theory $H_{BK}^*(Y)$ and verify that, first, it depends only on W (i.e., all such buildings are “homotopy equivalent”), and second, $H_{BK}^*(Y)$ is the associated graded of the coinvariant algebra of W under certain filtration. We also construct the dual homology “pre-ring” on Y. The…
5 Citations
A SURVEY OF THE ADDITIVE EIGENVALUE PROBLEM (WITH APPENDIX BY M. KAPOVICH)
The classical Hermitian eigenvalue problem addresses the following question: What are the possible eigenvalues of the sum A + B of two Hermitian matrices A and B, provided we fix the eigenvalues of A
A SURVEY OF THE ADDITIVE EIGENVALUE PROBLEM
The classical Hermitian eigenvalue problem addresses the following question: What are the possible eigenvalues of the sum A + B of two Hermitian matrices A and B, provided we x the eigenvalues of A
Additive Eigenvalue Problem (a survey), (With appendix by M. Kapovich)
The classical Hermitian eigenvalue problem addresses the following question: What are the possible eigenvalues of the sum A+B of two Hermitian matrices A and B, provided we fix the eigenvalues of A
The generalized triangle inequalities in thick Euclidean buildings of rank 2
We describe the set of possible vector valued side lengths of n-gons in thick Euclidean buildings of rank 2. This set is determined by a finite set of homogeneous linear inequalities, which we call

## References

SHOWING 1-10 OF 55 REFERENCES
Eigenvalue problem and a new product in cohomology of flag varieties
• Mathematics
• 2004
Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenous
The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra
• Mathematics
• 2002
In this paper we apply our results on the geometry of polygons in infinitesimal symmetric spaces, symmetric spaces and buildings, [KLM1, KLM2], to four problems in algebraic group theory. Two of
Extensions of Lipschitz maps into Hadamard spaces
• Mathematics
• 2000
Abstract. We prove that every $\lambda$-Lipschitz map $f : S \to Y$ defined on a subset of an arbitrary metric space X possesses a $c \lambda$-Lipschitz extension $\bar{f} : X \to Y$ for
The nil Hecke ring and cohomology of G/P for a Kac-Moody group G.
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1986
A ring R is constructed, which is very simply and explicitly defined as a functor of W together with the W-module [unk] alone and such that all these four structures on H(*)(G/B) arise naturally from the ring R.
Geometric invariant theory and the generalized eigenvalue problem
Let G be a connected reductive subgroup of a complex connected reductive group $\hat{G}$. Fix maximal tori and Borel subgroups of G and ${\hat{G}}$. Consider the cone $\mathcal{LR}(G,{\hat{G}})$
GEOMETRIC AND UNIPOTENT CRYSTALS
• Mathematics
• 2010
Let G be a split semisimple algebraic group over ℚ, g be the Lie algebra of G and U q (g) be the corresponding quantized enveloping algebra. Lusztig has introduced in [Lul] canonical bases for
Algebraic Polygons
• Mathematics
• 1996
In this paper we prove the following: Over each algebraically closed field K of Ž . characteristic 0 there exist precisely three algebraic polygons up to duality , namely the projective plane, the
On the Topology of Kac–Moody groups
We study the topology of spaces related to Kac–Moody groups. Given a Kac–Moody group over $$\mathbb C$$C, let $$\text {K}$$K denote the unitary form with maximal torus $${{\mathrm{T}}}$$T having
Operads in algebra, topology, and physics
• Mathematics
• 2002
'Operads are powerful tools, and this is the book in which to read about them' - ""Bulletin of the London Mathematical Society"". Operads are mathematical devices that describe algebraic structures
Polygons in Buildings and their Refined Side Lengths
• Mathematics
• 2004
As in a symmetric space of noncompact type, one can associate to an oriented geodesic segment in a Euclidean building a vector valued length in the Euclidean Weyl chamber Δeuc. In addition to the