2023/10/17 by S. Senthamarai Kannan, Kannan, S. Senthamarai, Arpita Nayek +1
Mathematics · #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2310.11091
openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let r and q be positive integers and n=qr+1. Let G = SL(n, ℂ) and T be a maximal torus of G. Let Pαr be the maximal parabolic subgroup of G corresponding to the simple root αr. Let ωr be the fundamental weight corresponding to αr. Let W be the Weyl group of G and WPαr be the Weyl group of Pαr. Let W^Pαr be the set of all minimal coset representatives of W/WPαr in W. Let wr,n (respectively, vr,n) be the minimal (respectively, maximal) element in W^P^αr such that wr,n(nωr) ≤ 0 (respectively, vr,n(nωr) ≥ 0). Let v ≤ vr,n and Xv_wr,n be the Richardson variety in Gr,n corresponding to v and wr,n. In this article, we give a sufficient condition on v such that the GIT quotient of Xv_wr,n for the action of T is the product of projective spaces with respect to the descent of the line bundle L(nωr).