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Conormal Varieties on the Cominuscule Grassmannian
Let G be a simply connected, almost simple group over an algebraically closed field k of characteristic p, where either p = 0 or p is an odd prime...
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Affine Grassmannians and Hessenberg Schubert Cells
We give an overview of the linear algebra, geometry, and combinatorics of affine Grassmannians along the lines of Fulton’s Young Tableaux for...
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Hyperplane sections of the projective bundle associated to the tangent bundle of \({\mathbb {P}}^2.\)
The aim of the note is to give a complete description of all the hyperplane sections of the projective bundle associated to the tangent bundle of
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Quiver Grassmannians of Type \(\widetilde {D}_{n}\), Part 2: Schubert Decompositions and F-polynomials
Extending the main result of Lorscheid and Weist (
2015 ), in the first part of this paper we show that every quiver Grassmannian of an indecomposable... -
Effective good divisibility of rational homogeneous varieties
We compute the effective good divisibility of a rational homogeneous variety, extending an earlier result for complex Grassmannians by Naldi and...
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Variations on a Theme of Schubert Calculus
In this tutorial, we provide an overview of many of the established combinatorial and algebraic tools of Schubert calculus, the modern area of...
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Matrix compression along isogenic blocks
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation...
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Schubert Polynomial Analogues for Degenerate Involutions
We survey the recent study of involution Schubert polynomials and a modest generalization that we call degenerate involution Schubert polynomials. We...
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A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory
We give a Chevalley formula for an arbitrary weight for the torus-equivariant K -group of semi-infinite flag manifolds, which is expressed in terms of...
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Geometric Vertex Decomposition, Gröbner Bases, and Frobenius Splittings for Regular Nilpotent Hessenberg Varieties
We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties by studying the special case of regular nilpotent...
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A note on toric degeneration of a Bott–Samelson–Demazure–Hansen variety
In this paper, we study the geometry of toric degeneration of a Bott–Samelson–Demazure–Hansen (BSDH) variety, which was algebraically constructed by...
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A topological proof of the Shapiro–Shapiro conjecture
We prove a generalization of the Shapiro–Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We...
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Understanding Schubert’s book (II)
In this paper, we give rigorous justification of the ideas put forward in §20, Chapter 4 of Schubert’s book; a section that deals with the...
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Rational Cherednik Algebras and Schubert Cells
The representation theory of rational Cherednik algebras of type A at t = 0 gives rise, by considering supports, to a natural family of smooth...
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A filtration on the cohomology rings of regular nilpotent Hessenberg varieties
Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent...
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Product structure and regularity theorem for totally nonnegative flag varieties
The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this...
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Euler characteristics in the quantum K-theory of flag varieties
We prove that the sheaf Euler characteristic of the product of a Schubert class and an opposite Schubert class in the quantum K -theory ring of a...
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Closures of K-orbits in the Flag Variety for \(\mathrm {Sp}(2n,\mathbb {R})\)
We give a pattern avoidance criterion to classify the orbits of $$\mathbb {GL}(n,{\mathbb C})$$ on the flag variety of $$\mathrm {Sp}(2n,{\mathbb...