论文标题
仿射RSK对应和零级极重模块的晶体
Affine RSK correspondence and crystals of level zero extremal weight modules
论文作者
论文摘要
我们给出了Robison-Schensted-Knuth（RSK）对应的仿真，该对应概括了Chmutov-Pylyavskyy-Yudovina的仿射Robinson-Schensted。 Aggine RSK地图向一对tableaux $（p，q）$的一般呈$（m，n）$发送的广义仿射排列，其中$ p $属于一个级别的kirillov-reshetikhin type $ a_ a_ a_ a_ a_ a _ {m-1}^（m-1}^{（1）$ s $ a crivers a type $ a_ kirillov-reshetikhin的张量$ a_ {n-1}^{（1）} $当$ m，n \ ge 2 $。我们考虑了两种类型的仿生晶体结构$ a_ {m-1}^{（1）} $和$ a_ {n-1}^{（1）} $上的$ a_ {（1）} $，并在一组广义仿射排列上$，并表明仿射RSK映射保留了水晶等价。我们还提供了双仿射robison-Schensted-Knuth对应。
We give an affine analogue of the Robison-Schensted-Knuth (RSK) correspondence, which generalizes the affine Robinson-Schensted correspondence by Chmutov-Pylyavskyy-Yudovina. The affine RSK map sends a generalized affine permutation of period $(m,n)$ to a pair of tableaux $(P,Q)$ of the same shape, where $P$ belongs to a tensor product of level one perfect Kirillov-Reshetikhin crystals of type $A_{m-1}^{(1)}$, and $Q$ belongs to a crystal of extremal weight module of type $A_{n-1}^{(1)}$ when $m,n\ge 2$. We consider two affine crystal structures of types $A_{m-1}^{(1)}$ and $A_{n-1}^{(1)}$ on the set of generalized affine permutations, and show that the affine RSK map preserves the crystal equivalence. We also give a dual affine Robison-Schensted-Knuth correspondence.
