2023/07/18 by Coskun, Izzet, Eken, Demir, Yun, Chris
#14M15 #14M17. Secondary: 14L35 #51N30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14L30 #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2307.09265
In this paper, we introduce tree varieties as a natural generalization of products of partial flag varieties. We study orbits of the PGL action on tree varieties. We characterize tree varieties with finitely many PGL orbits, generalizing a celebrated theorem of Magyar, Weyman and Zelevinsky. We give criteria that guarantee that a tree variety has a dense PGL orbit and provide many examples of tree varieties that do not have dense PGL orbits. We show that a triple of two-step flag varieties F(k1, k2; n)3 has a dense PGL orbit if and only if k1 + k2 \not= n.