论文标题
在Drinfeld模块化形式上，高级VI的模块化形式：与系数形式相关的简单复合物
On Drinfeld modular forms of higher rank VI: The simplicial complex associated with a coefficient form
论文作者
论文摘要
系数形式\（{} _ {a} \ ell_ {k} \）和para-eisenstein系列\（α_{k} \）是简单的Drinfeld模块化形式。我们研究所附的简单复合物\（\ Mathcal {bt}^{r}（{} _ {a} _ {a} \ ell_ {k}）\）和\（\ Mathcal {bt}^r} \（\ Mathcal {bt}^{r} \）它们已连接（如果等级\（r \）大于2），则在\（\ Mathcal {bt}^{r} \）中对编码1的均等1，无边界，并满足对称属性，在dynkin diagram的非实用性下的对称性属性。
The coefficient forms \( {}_{a} \ell_{k} \) and the para-Eisenstein series \(α_{k}\) are simplicial Drinfeld modular forms. We study the attached simplicial complexes \(\mathcal{BT}^{r}( {}_{a} \ell_{k})\) and \(\mathcal{BT}^{r}(α_{k})\), which are full subcomplexes of the Bruhat-Tits building \(\mathcal{BT}^{r}\) of \( \mathrm{PGL}(r, K_{\infty})\). They are connected (if the rank \(r\) is larger than 2), strongly equidimensional of codimension 1 in \(\mathcal{BT}^{r}\), boundaryless, and satisfy a symmetry property under the non-trivial involution of the Dynkin diagram \(A_{r-1}\).
