AI 中文总结
针对非阿基米德局部域上特定群，引入计算奥伯特对偶新算法，采用自底向上方法且保持表示温和性，能为余温表示新性质归纳证明，给出温和分量描述及对偶公式。
AI 中文摘要
设\(F\)为特征\(0\)的非阿基米德局部域，\(G\)为\(\Sp_{2n}(F)\)或\(\SO_{2n + 1}(F)\)。我们引入一种新算法来计算朗兰兹数据层面的奥伯特对偶。该算法是近期拉纳德 - 明格斯算法的对偶，采用自底向上而非自顶向下的方法，内部计算严格保持表示的温和性。这自然产生了余温表示的新构造性特征，能为余温表示新性质进行归纳证明，给出其温和分量的精确描述并建立一大类温和表示的显式对偶公式。
英文摘要
Let $F$ be a non-archimedean local field of characteristic 0, and let $G$ be either $\mathrm{Sp}_{2n}(F)$ or $\mathrm{SO}_{2n+1}(F)$. We introduce a new algorithm to compute the Aubert dual at the level of Langlands data. This algorithm acts as the dual to the recent Lanard-Mínguez algorithm. It fundamentally differs in two ways: it follows a bottom-up approach rather than a top-down one, and its internal computations strictly preserve the temperedness of the representations. Consequently, this approach naturally yields a new constructive characterization of co-tempered representations. By operating exclusively within the realm of tempered data, this algorithm enables inductive proofs of new properties for co-tempered representations. In particular, we provide a precise description of their tempered components and establish an explicit duality formula for a large class of tempered representations.
Comments53 pages, comments are welcome (V2 just for a little change in the title)
