R. M. Green

collaborators

3 papers

math.CO2026

Generalized Rothe diagrams for orthogonal roots

R. M. Green, Tianyuan Xu

Let $U$ be a set of positive roots of type $A D E$ , and let $Ω_{U}$ be the set of all maximum-cardinality orthogonal subsets of $U$ . We associate a generalized Rothe diagram to each el…

math.CO2026

Branching rules of minuscule representations via a new partial order

R. M. Green, Tianyuan Xu

We introduce a new partial order on the set of all antichains of a fixed size in any poset. When applied to minuscule posets, these partial orders give rise to distributive lattice…

math.CO2025

Orthogonal roots, Macdonald representations, and quasiparabolic sets

R. M. Green, Tianyuan Xu

Let $W$ be a simply laced Weyl group of finite type and rank $n$ . If $W$ has type $E_{7}$ , $E_{8}$ , or $D_{n}$ for $n$ even, then the root system of $W$ has subsystems of type $n A_{1}$ . Th…