Littlewood-Richardson-Sundaram表的辛左伴表与Kwon性质
The symplectic left companion of a Littlewood-Richardson-Sundaram tableau and the Kwon property
AI总结：
本文通过构造LR-Sundaram表的左伴表，揭示了Kwon辛性质与辛Gelfand-Tsetlin模式之间的关系。
摘要：
作为Littlewood-Richardson（LR）交换子的巧合以及Kumar-Torres分支模型通过Kushwaha-Raghavan-Viswanath标记蜂窝的后果，我们解决了Lecouvey-Lenart关于Kwon和Sundaram分支模型之间双射的猜想，该猜想涉及一般线性群GL_{2n}(C)和辛群Sp_{2n}(C)的配对。特别是，得益于Henriques-Kamnitzer的gl_n晶体交换子，我们认识到LR-Sundaram表的左伴表由Kwon辛条件所特征化。我们现在使用构造LR-Sundaram表的左Gelfand-Tsetlin模式或左伴表来展示Kwon辛性质，这是其右伴表上的旗帜的镜像。这等同于将Berenstein-Gelfand-Zelevinsky LR模型对Gelfand-Tsetlin模式的限制，解释为辛Gelfand-Tsetlin模式作为LR-Sundaram表的左伴表。
英文摘要：
As a consequence of the Littlewood-Richardson (LR) commuters coincidence and the Kumar-Torres branching model via Kushwaha-Raghavan-Viswanath flagged hives, we have solved the Lecouvey- -Lenart conjecture on the bijections between the Kwon and Sundaram branching models for the pair $({GL}_{2n}(\mathbb{C}), {Sp}_{2n}(\mathbb{C})) $ consisting of the general linear group ${GL}_{2n}(\mathbb{C})$ and the symplectic group ${Sp}_{2n}(\mathbb{C})$. In particular, thanks to the Henriques-Kamnitzer $gl_n$-crystal commuter, we have recognized that the left companion of an LR-Sundaram tableau is characterized by the Kwon symplectic condition. We now use the construction of the left Gelfand-Tsetlin pattern, or left companion tableau, of an LR-Sundaram tableau to exhibit the Kwon symplectic property, a mirror of the flag on its right companion tableau. This is equivalent to the restriction of the Berenstein-Gelfand-Zelevinsky LR model, on the interpretation of Gelfand-Tsetlin patterns, to symplectic Gelfand-Tsetlin patterns as left companions of LR-Sundaram tableaux.
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