Representation theory of Drinfeld modular forms of level T

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• 作者：Enrico Varela Roldá ; n ^{varela@math.uni-sb.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11F52 ; secondary ; 20C20 ; 20G40 ; 11E57
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：63-92
• 全文大小：477 K

文摘

This paper expands upon our results for the arithmetic of Drinfeld modular forms of level T [12] by providing an interpretation from a representation theoretic point of view.

We identify GL(2,F_q)$\mathrm{GL}(2,{\mathbb{F}}_q)$-modules that arise naturally from the theory of Drinfeld modular forms of level T   with classical GL(2,F_q)$\mathrm{GL}(2,{\mathbb{F}}_q)$-modules. Using the arithmetic of the so-called modified Eisenstein series all isomorphisms are stated explicitly.

In particular, we examine the close connection between Drinfeld modular forms of level T   and the theory of symmetric powers of the tautological representation of GL(2,F_q)$\mathrm{GL}(2,{\mathbb{F}}_q)$ described in previous work [13].