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Showing 1 to 7 of 7 for “"Schubert Varieties"”.
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Combinatorics in Schubert varieties and Specht modules
… In the first part of the thesis, we link Schubert varieties in the full flag variety with hyperplane arrangements. Schubert varieties are parameterized by elements of the Weyl group. For each element of the Weyl group, we construct certain hyperplane arrangement. We show that the …
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Matrix Schubert varieties for the affine Grassmannian
Schubert calculus has become an indispensable tool for enumerative geometry. It concerns the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The …
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Specht modules and Schubert varieties for general diagrams
… other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these objects to allow for not just Young diagrams but arbitrary collections of boxes or, equally well, bipartite graphs. We will then provide …
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Diagrams and reduced decompositions for cominuscule flag varieties and affine Grassmannians.
… of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first case, an abbreviated computation of relative R-polynomials. From this, we show that these polynomials can be obtained from unlabelled intervals, and more …
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Derived categories of coherent sheaves on rational homogeneous manifolds
… of complete exceptional sequences on toric varieties. Starting point of the present work is a conjecture of F. Catanese which says that on every rational homogeneous manifold $X=G/P$, where $G$ is a connected complex semisimple Lie group and $P\subset G$ a parabolic subgroup, there should …
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Prism tableaux and alternating sign matrices
A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w in Fl(C^n). Schubert polynomials are indexed by elements of the symmetric group …
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The Combinatorial Curve Neighborhoods of Affine Flag Manifold in Type A<sub>n-1</sub><sup>(1)</sup>
Let X be the affine flag manifold of Lie type A<sub>n-1</sub><sup>(1)</sup> where n ≥ 3 and let W<sub>aff</sub> be the associated affine Weyl group. The moment graph for X encodes the torus fixed points (which are elements of the affine Weyl group W<sub>aff</sub> and the torus stable curves in X. …