R. M. Green

collaborators

3 papers

math.CO2025

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.CO2024

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…

math.CO2024

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…