论文标题
限制全球基础和罗德斯定理
Restriction of Global Bases and Rhoades's Theorem
论文作者
论文摘要
结果表明，如果$λ$是$ \ mathfrak {sl} _k $的基本权重的多个，则是不可删除的$ u_q（\ mathfrak {sl} _k）$ v^λ$具有最高权重$λ$的不可约束的全球基础的全球较低基础。 $ u_q（\ mathfrak {sl} _ {k-1}）$ - 表示$ v^λ$ to $ u_q（\ mathfrak {\ mathfrak {sl} _ {k-1}）的限制中出现的表示。然后从贝伦斯坦（Zelevinsky）描述了$ v^λ$的双重规范基础上对长周期的作用的描述 - Zelevinsky对长元素的作用的描述。这可以简短证明Rhoades在晋升下固定的Tableaux结果的结果，这将其与STEMBRIDGE在疏散下固定的Tableaux的结果直接相关。
It is shown that if $λ$ is a multiple of a fundamental weight of $\mathfrak{sl}_k$, the lower global basis of the irreducible $U_q(\mathfrak{sl}_k)$-representation $V^λ$ with highest weight $λ$ comprises the disjoint union of the lower global bases of the irreducible $U_q(\mathfrak{sl}_{k-1})$-representations appearing in the decomposition of the restriction of $V^λ$ to $U_q(\mathfrak{sl}_{k-1})$. Rhoades's description of the action of the long cycle on the dual canonical basis of $V^λ$ is then deduced from Berenstein--Zelevinsky's description of the action of the long element. This yields a short proof of Rhoades's result on tableaux fixed under promotion which directly relates it to Stembridge's result on tableaux fixed under evacuation.
