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<p>This article proves an alcove walk description of intersections of Schubert cells and partially semi-infinite orbits (depending on a choice of parabolic subgroup) in the affine Grassmannian of a split connected reductive group (we call these intersections <i>parabolic Mirković-Vilonen intersections</i>). We deduce from this a parameterization of the irreducible components of the maximal possible dimension in these intersections by the alcove walks of maximal possible dimension. As a consequence we present a new combinatorial description of branching to Levi subgroups of irreducible highest weight representations, and in particular, we give a new algorithm for computing the characters of such representations.</p>

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Alcove Walk Models for Parabolic Mirković-Vilonen Intersections and Branching to Levi Subgroups

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  • 发表日期：

    2026年5月19日

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  • Thomas J. Haines

摘要

This article proves an alcove walk description of intersections of Schubert cells and partially semi-infinite orbits (depending on a choice of parabolic subgroup) in the affine Grassmannian of a split connected reductive group (we call these intersections parabolic Mirković-Vilonen intersections). We deduce from this a parameterization of the irreducible components of the maximal possible dimension in these intersections by the alcove walks of maximal possible dimension. As a consequence we present a new combinatorial description of branching to Levi subgroups of irreducible highest weight representations, and in particular, we give a new algorithm for computing the characters of such representations.