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Singularities of Affine Schubert Varieties [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type A_l^{(1)}). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent ...
Jochen Kuttler, Venkatramani Lakshmibai
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An algorithm for computing Schubert varieties of best fit with applications [PDF]
Frontiers in Artificial Intelligence, 2023 We propose the geometric framework of the Schubert variety as a tool for representing a collection of subspaces of a fixed vector space. Specifically, given a collection of l-dimensional subspaces V1, …, Vr of ℝn, represented as the column spaces of ...
Karim Karimov +2 more
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Staircase diagrams and the enumeration of smooth Schubert varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert varieties are in bijection with a new combinatorial data ...
Edward Richmond, William Slofstra
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Total positivity for the Lagrangian Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index ...
Rachel Karpman
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Which Schubert varieties are local complete intersections? [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We characterize by pattern avoidance the Schubert varieties for $\mathrm{GL}_n$ which are local complete intersections (lci). For those Schubert varieties which are local complete intersections, we give an explicit minimal set of equations cutting out ...
Henning Úlfarsson, Alexander Woo
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The Prism tableau model for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1; x2; : : :]. We suggest the prism tableau model for these polynomials.
Anna Weigandt, Alexander Yong
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Rational smoothness and affine Schubert varieties of type A [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The study of Schubert varieties in G/B has led to numerous advances in algebraic combinatorics and algebraic geometry. These varieties are indexed by elements of the corresponding Weyl group, an affine Weyl group, or one of their parabolic quotients ...
Sara Billey, Andrew Crites
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$q$-Rationals and Finite Schubert Varieties
Comptes Rendus. Mathématique, 2023 The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. Some combinatorial interpretations are already known, namely as the rank generating functions for certain ...
Ovenhouse, Nicholas
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Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
Forum of Mathematics, Pi, 2021 We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${\mathbb K}$ of characteristic $\neq 2$ from scratch.
Syu Kato
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Interval positroid varieties and a deformation of the ring of symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Define the interval rank $r_[i,j] : Gr_k(\mathbb C^n) →\mathbb{N}$ of a k-plane V as the dimension of the orthogonal projection $π _[i,j](V)$ of V to the $(j-i+1)$-dimensional subspace that uses the coordinates $i,i+1,\ldots,j$.
Allen Knutson, Mathias Lederer
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