Let \( {\overline{\mathrm{X}}}_{\uplambda} \) be the closure of the I-orbit \( {\overline{\mathrm{X}}}_{\uplambda} \) in the affine Grassmanian Gr of a simple algebraic group G of adjoint type, where I is the Iwahori subgroup and λ is a coweight of G. We find a simple algorithm which describes the set Ψ(λ) of all I-orbits in \( {\overline{\mathrm{X}}}_{\uplambda} \) in terms of coweights. We introduce R-operators (associated to positive roots) on the coweight lattice of G, which exactly describe the closure relation of I-orbits. These operators satisfy Braid relations generically on the coweight lattice. We also establish a duality between the set Ψ(λ) and the weight system of the level one affine Demazure module

让\（{\划线{\ mathrm {X}}} _ {\ uplambda} \）是I-轨道关闭\（{\划线{\ mathrm {X}}} _ {\ uplambda} \）在伴随类型的简单代数群G的仿射Grassmanian Gr ，其中I是Iwahori子群，λ是G的权重。我们找到了一种简单的算法，以权重来描述\（{\ overline {\ mathrm {X}}} _ {\ uplambda} \）中所有I轨道的集合Ψ（λ）。我们在G的权重格上引入R-运算符（与正根相关），它准确地描述了I轨道的闭合关系。这些算子通常在重重格上满足编织关系。我们还建立了集合Ψ（λ）与一级仿射Demazure模块的权重系统之间的对偶