论文标题
Young晶格上的上下操作员
Up- and Down-Operators on Young's Lattice
论文作者
论文摘要
U_I $ $ U_I $和DOWN-ORERATORS $ D_I $（由Fomin作为Schur运营商引入）通过分区行动，如果可能的话，将盒子添加/删除/从$ i $ th列中添加/卸下盒子。众所周知，仅$ u_i $就满足了（局部）构成的关系，而现在的作者最近表明，学位的关系最多足以描述上运营商之间的所有关系。在这里，我们将上和下操作员共同产生的代数表征，表明它只能使用二次关系来呈现。
The up-operators $u_i$ and down-operators $d_i$ (introduced as Schur operators by Fomin) act on partitions by adding/removing a box to/from the $i$th column if possible. It is well known that the $u_i$ alone satisfy the relations of the (local) plactic monoid, and the present authors recently showed that relations of degree at most 4 suffice to describe all relations between the up-operators. Here we characterize the algebra generated by the up- and down-operators together, showing that it can be presented using only quadratic relations.
