AbstractLet $$\Gamma _n(\mathcal {\scriptstyle {O}}_{\mathbb {K}})$$
Γ
n
(
O
K
)
denote the Hermitian modular group of degree n over an imaginary quadratic number field $$\mathbb {K}$$
K
and $$\Delta _{n,\mathbb {K}}^*$$
Δ
n
,
K
∗
its maximal discrete extension in the special unitary group $$SU(n,n;\mathbb {C})$$
S
U
(
n
,
n
;
C
)
. In this paper we study the action of $$\Delta _{n,\mathbb {K}}^*$$
Δ
n
,
K
∗
on Hermitian theta series and Maaß spaces. For $$n=2$$
n
=
2
we will find theta lattices such that the corresponding theta series are modular forms with respect to $$\Delta _{2,\mathbb {K}}^*$$
Δ
2
,
K
∗
as well as examples where this is not the case. Our second focus lies on studying two different Maaß spaces. We will see that the new found group $$\Delta _{2,\mathbb {K}}^*$$
Δ
2
,
K
∗
consolidates the different definitions of the spaces.
Hermitian Theta Series and Maaß Spaces Under the Action of the Maximal Discrete Extension of the Hermitian Modular Group