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arXiv · 2208.09908

On Drinfeld modular forms of higher rank VI: The simplicial complex associated with a coefficient form

Ernst-Ulrich Gekeler
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Abstract

The coefficient forms \( {}_{a} \ell_{k} \) and the para-Eisenstein series \(\alpha_{k}\) are simplicial Drinfeld modular forms. We study the attached simplicial complexes \(\mathcal{BT}^{r}( {}_{a} \ell_{k})\) and \(\mathcal{BT}^{r}(\alpha_{k})\), 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 \(A_{r-1}\).

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Ernst-Ulrich Gekeler. 2022-08-21. On Drinfeld modular forms of higher rank VI: The simplicial complex associated with a coefficient form. https://arxiv.org/abs/2208.09908

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