The principal series 2-representation for ${\mathrm{GL}}_n\times {\mathrm{GL}}_n$ over a 2-dimensional local field

Xuecai Ma, Jingwen Zhu

Let $F={\mathbb{F}}_q((u))((t))$ and $H={\mathrm{GL}}_n(F{)}_L\times {\mathrm{GL}}_n(F{)}_R$. An ordered tuple $\alpha =({\alpha }_1,\dots ,{\alpha }_n)$ defines a cross-$K_2$ multiplier on the doubled Borel. Twi…