朗兰兹对偶与不变微分算子：SL(2n+1)的情形
Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)
AI总结：
本文在朗兰兹对偶与不变微分算子间搭建桥梁，基于哈里什-钱德拉的半单李群表示理论，针对SL(2n+1)的情形展开研究，此前已研究SL(2n)的情形，两类群的表示理论存在差异。
AI中文摘要：
近期，我们开始在朗兰兹对偶的两种情形之间搭建桥梁。朗兰兹对偶是数学研究中最具影响力的课题之一，具有多种不同的表现形式和有影响力的子课题。然而，至今似乎有一个与朗兰兹纲领无关的课题，即不变微分算子。这一情况颇为奇怪，因为这两个课题都深深植根于哈里什-钱德拉的半单李群表示理论。我们已从群SL(2n)的情形入手开展研究，本文则处理群SL(2n+1)的情形；上述两个群虽具有相似性，但它们的表示理论却存在显著差异。
英文摘要：
Recently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invariant differential operators. That is strange since both items are deeply rooted in Harish-Chandra's representation theory of semisimple Lie groups. We started with the case of the group ~$SL(2n)$. In the present paper we deal with the group $SL(2n+1)$. The two mentioned groups are similar, but their representation theories is rather different.
