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On the Continuity of the Tangent Cone to the Determinantal Variety
Tangent and normal cones play an important role in constrained optimization to describe admissible search directions and, in particular, to formulate...
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Probabilistic Schubert Calculus: Asymptotics
In the recent paper Bürgisser and Lerario (Journal für die reine und angewandte Mathematik (Crelles J), 2016) introduced a geometric framework for a...
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Structure constants in equivariant oriented cohomology of flag varieties
We introduce generalized Demazure operators for the equivariant oriented cohomology of the flag variety, which have specializations to various...
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Schubert Derivations on the Infinite Wedge Power
The Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of...
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WHITTAKER FUNCTIONS FROM MOTIVIC CHERN CLASSES
We prove a motivic analogue of the Weyl character formula, computing the Euler characteristic of a line bundle on a generalized ag manifold G / B ...
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Proper elements of Coxeter groups
We extend the notion of proper elements to all finite Coxeter groups. For all infinite families of finite Coxeter groups we prove that the...
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Minuscule Schubert Calculus and the Geometric Satake Correspondence
We describe a relationship between work of Gatto, Laksov, and their collaborators on realizations of (generalized) Schubert calculus of...
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Permutation actions on Quiver Grassmannians for the equioriented cycle via GKM-theory
In our previous work, we equipped quiver Grassmannians for nilpotent representations of the equioriented cycle with an action of an algebraic torus....
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COTANGENT BUNDLES OF PARTIAL FLAG VARIETIES AND CONORMAL VARIETIES OF THEIR SCHUBERT DIVISORS
Let P be a parabolic subgroup in G = SL n ( k ), for k an algebraically closed field. We show that there is a G -stable closed subvariety of an affine...
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On a Conjecture of Fulton on Isotropic Grassmannians
In this note, we confirm a positivity conjecture of Fulton (Conjecture 1 below) for isotropic Grassmannians...
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A Proof of the Refined PRV Conjecture via the Cyclic Convolution Variety
In this brief note we illustrate the utility of the geometric Satake correspondence by employing the cyclic convolution variety to give a simple...
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Hessenberg varieties of parabolic type
This paper studies the geometry and combinatorics of three interrelated varieties: Springer fibers, Steinberg varieties, and parabolic Hessenberg...
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Understanding Schubert’s Book (III)
In §13 of Schubert’s famous book on enumerative geometry, he provided a few formulas called coincidence formulas, which deal with coincidence points...
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Relative Bott–Samelson Varieties
We prove that, defined with respect to versal flags, the product of two relative Bott–Samelson varieties over a flag bundle is a resolution of...
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Demazure crystals and the Schur positivity of Catalan functions
Catalan functions, the graded Euler characteristics of certain vector bundles on the flag variety, are a rich class of symmetric functions which...
