Year: 2023
Type: preprint
Abstract: 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 $F(k_1, k_2; n)^3$ has a dense PGL orbit if and only if $k_1 + k_2 \not= n$.
Source: arXiv (Cornell University)
Authors: Coskun, Izzet, Eken, Demir, Yun, Chris
Institutions: University of Illinois Chicago, University of Michigan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4384811591