2024/05/27 by Haines, Thomas J.
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2405.17174
This article establishes alcove walk models for intersections of Schubert varieties and partially semi-infinite orbits in the affine Grassmannian of a split reductive group (we call such intersections parabolic Mirković-Vilonen intersections). More precisely, we describe explicit cellular pavings of these intersections, indexed by certain positively-folded alcove walks. We prove a parametrization of the irreducible components of maximal possible dimension, in terms of alcove walks of maximal possible dimension. We then deduce 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.