# The residual spectrum of $U(n,n)$; contribution from Borel subgroups

Document Type : Special Issue of BIMS in Honor of Professor Freydoon Shahidi

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Abstract

‎In this paper we study the residual spectrum of the quasi-split unitary group $G=U(n,n)$ defined over a number field $F$‎, ‎coming from the Borel subgroups‎, ‎$L_{dis}^2(G(F)\backslash G(\Bbb A))_T$‎. ‎Due to lack of information on the local results‎, ‎that is‎, ‎the image of the local intertwining operators of the principal series‎, ‎our results are incomplete‎. ‎However‎, ‎we describe a conjecture on the residual spectrum and prove a certain special case by using the Knapp-Stein $R$-group of the unitary group‎.

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### History

• Receive Date: 15 May 2017
• Revise Date: 01 October 2017
• Accept Date: 19 May 2017