Results 11 to 20 of about 761 (218)
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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DEGENERATE SCHUBERT VARIETIES IN TYPE A [PDF]
Transformation Groups, 2020 We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed a Schubert variety in a partial flag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated to a rectangular element
Chirivì Rocco +2 more
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Toric matrix Schubert varieties and root polytopes (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Start with a permutation matrix π and consider all matrices that can be obtained from π by taking downward row operations and rightward column operations; the closure of this set gives the matrix Schubert variety Xπ.
Laura Escobar, Karola Mészáros
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Beilinson–Drinfeld Schubert varieties and global Demazure modules
Forum of Mathematics, Sigma, 2021 We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.
Ilya Dumanski +2 more
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An equivariant rim hook rule for quantum cohomology of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis.
Elizabeth Beazley +2 more
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Schubert Varieties and Free Braidedness [PDF]
Transformation Groups, 2004 We give a simple necessary and sufficient condition for a Schubert variety $X_w$ to be smooth when $w$ is a freely braided element of a simply laced Weyl group; such elements were introduced by the authors in a previous work (math.CO/0301104). This generalizes in one direction a result of Fan concerning varieties indexed by short-braid avoiding ...
Green, R. M., Losonczy, J.
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A noncommutative geometric LR rule [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian.
Edward Richmond +2 more
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Schubert varieties, inversion arrangements, and Peterson translation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+
William Slofstra
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Which Schubert Varieties are Hessenberg Varieties?
Transformation Groups, 2023 34 ...
Laura Escobar +2 more
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