论文标题
与laurent多项式的Kac-Moody组相关的双载
Twin masures associated with Kac-Moody groups over Laurent polynomials
论文作者
论文摘要
令$ \ mathfrak {g} $为拆分还原组，$ \ mathbb {k} $是一个字段，$ \ varpi $是不确定的。为了研究$ \ Mathfrak {g}（\ Mathbb {k} [\ varpi，\ varpi^{ - 1}]））$和$ \ Mathfrak {G}（\ Mathbb {k {k}（\ varpi）（\ varpi）） \ Mathcal {i} _ \ oplus \ times \ times \ Mathcal {i} _ \ ominus $，其中$ \ Mathcal {i} _ \ oplus $和$ \ Mathcal {i} _ \ ominus $通过a''''''''''''与之相关。确保概括了bruhat-tits建筑物，该建筑适合于对质量领域的Kac-Moody群体进行研究。由Dinakar Muthiah在与Kac-Moody群体相关的Kazhdan-Lusztig多项式上的工作的动机，我们研究了$ \ Mathfrak {g}的动作（\ Mathbb {k} $ \ mathfrak {g}（\ mathbb {k}（\ varpi，\ varpi^{ - 1}））$在其''twin masure''上，当$ \ mathfrak {g} $是一个分裂的kac-moody群体时，而不是一个还原的组。
Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and $\varpi$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on their twin building $\mathcal{I} = \mathcal{I}_\oplus\times \mathcal{I}_\ominus$, where $\mathcal{I}_\oplus$ and $\mathcal{I}_\ominus$ are related via a ''codistance''. Masures are generalizations of Bruhat-Tits buildings adapted to the study of Kac-Moody groups over valued fields. Motivated by the work of Dinakar Muthiah on Kazhdan-Lusztig polynomials associated with Kac-Moody groups, we study the action of $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi,\varpi^{-1}))$ on their ''twin masure'', when $\mathfrak{G}$ is a split Kac-Moody group instead of a reductive group.
