Coxeter system of planes are sets of injectivity for the twisted spherical means on ${\mathbb{C}}^n$

In this article, we prove that any pair of perpendicular planes is a set of injectivity for the twisted spherical means (TSM) for $L^p(\mathbb C^n) (n\geq2)$with$1\leq p\leq2.$ Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for $L^p({\mathbb{C}}^n)\mathrm{.}$ We further observe that a set $S_R^{2n-1}\times \mathbb{C}$ is a set of injectivity for the TSM for a ceratin class of functions on ${\mathbb{C}}^{n+1}\mathrm{.}$