The principal series 2-representation for GLn×GLn over a 2-dimensional local field
Xuecai Ma, Jingwen Zhu
Abstract
Let F=Fq((u))((t)) and H=GLn(F)L×GLn(F)R. An ordered tuple α=(α1,…, αn) defines a cross-K2 multiplier on the doubled Borel. Twisted equivariantization then yields an exact uniformly smooth categorical principal series 2-representation of H. For unitary parameters, the R((X))-measure gives a positive Hom-valued formal Hermitian inner product on the spherical part. These constructions provide two-dimensional categorical analogues of selected unramified structures.
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