Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields by Hatice Boylan

Author:Hatice Boylan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Remark

Let be an -FQM with level . By (2.3) and also Lemma 2.70 we have that acts on via

Here δ(A) is any element of which satisfies (2.32). Using the first remark after Definition 2.55 and Proposition 2.2 we have that also acts on the space .

On the other hand, since is a -module (see Sect. 2.2), the group acts on via (see (2.3))

where ρ is the representation afforded by -module . But from Theorem 2.8 we know that ρ and δ differ only by a constant. Therefore, the action of on the spaces and coincide.

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