Cominuscule Tableau Combinatorics
نویسندگان
چکیده
منابع مشابه
1 1 A ug 2 00 6 A COMBINATORIAL RULE FOR ( CO ) MINUSCULE SCHUBERT CALCULUS
We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G/P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of [Proc-tor '04], thereby giving a generalization of the [Schützenberger '77] jeu de taquin formulation of the Littlewood-Richardson rule that compu...
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In this paper we explore the combinatorics of the nonnegative part (G/P )≥0 of a cominuscule Grassmannian. For each such Grassmannian we define Γ -diagrams — certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P )≥0. In the classical cases, we describe Γ -diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can...
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We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G/P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of [Proc-tor '04], thereby giving a generalization of the [Schützenberger '77] jeu de taquin formulation of the Littlewood-Richardson rule that compu...
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A tableau inversion is a pair of entries in row-standard tableau T that lie in the same column of T yet lack the appropriate relative ordering to make T columnstandard. An i-inverted Young tableau is a row-standard tableau along with precisely i inversion pairs. Tableau inversions were originally introduced by Fresse to calculate the Betti numbers of Springer fibers in Type A, with the number o...
متن کاملThe Recursive Nature of Cominuscule Schubert Calculus
The necessary and sufficient Horn inequalities which determine the nonvanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson coefficients on smaller Grassmannians. We show how non-vanishing in the Schubert calculus for cominuscule flag varieties is similarly recursive. For these var...
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