Let $F$ be a $p$-adic local field and $W$ be a 2n-dimensional symplectic space over $F$. Let $G_n$ be the isometry group of $W$ and $B_n$ be the Borel subgroup of $G_n$. Then the maximal torus $T_n$ of $B_n$ is isomorphic to $(GL_1)^n$. Let $\pi$ be an irreducible quotient of $Ind_{B_n(F)}^{G_n(F)} (\chi_1 \boxtimes \cdots \boxtimes \chi_n)$, the normalized induction of a character $\chi_1 \boxtimes \cdots \boxtimes \chi_n$ of $T_n$ to $G_n$.
Let $|\chi_i|=|\cdot|^{s_i}$ for some $s_i \in \mathbb{R}$. If $s_{i_0} \ge 1$ for some $i_0$ and other $s_i$' are in $-\frac{1}{2}<s_i<\frac{1}{2}$, it seems that author claims that $\pi$ is non-generic. But I don't know why it is. I just guess that there might be some general criterion for determining generality and it violates it.
I appreciate if you shed me a light on this!
Thank you very much in advance.
