Abstract: In algebraic geometry, Schubert varieties offer insights into Intersection Theory where their fundamental classes form a basis for the Grassmannian’s cohomology ring. Richardson varieties are the transverse intersection of two Schubert varieties. One of the most intriguing aspects of Schubert varieties and Richardson varieties is how their geometric properties can often be described by the combinatorics of the Weyl group. Given a linear algebraic group $G$, a Borel subgroup $B$, and parabolic subgroup $P$ containing $B$, there is a natural projection map from the flag variety $G/B$ to the flag variety $G/P$. As it turns out, whether or not the restriction of this map to a Richardson variety has equidimensional fibers, can be characterized combinatorially via the Weyl group. In this talk, we describe these combinatorial conditions and offer an efficient means of checking them in codimension 1.
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