The question of which House member will serve on the reconstituted Shelby County Public Building Authority, which will oversee construction of a new NBA arena, has apparently been resolved in favor of Democratic state representative Larry Miller , who represents a predominantly African-American district in North Memphis. Miller had expressed interest in the appointment and had been endorsed by state House Speaker Jimmy Naifeh of Covington. By informal agreement with Memphis Mayor Willie Herenton, who had previously appointed state Senator John Ford to the PBA, the appointment of a House member will be the prerogative of Shelby County Mayor Jim Rout. On Friday, during a break in legislative action, Millers only declared rival, Rep. Tre Hargett, a white Republican who represents the Bartlett area, had a conversation with Naifeh on the House floor about the issue, and that talk apparently decided him to withdraw his own candidacy (which had been formally proposed last week by his House GOP colleague, Paul Stanley of Germantown). In a letter to Rout prepared at noon Friday, Hargett informed the county mayor, I regret to inform you that I withdraw my name for consideration as your House nominee to the Public Building Authority.. . . Citing the press of (including the still unresolved state budget), Hargett proceeded to say, I know Representative Larry Miller has indicated a willingness to serve on this important civic body.While Representative ;Miller and I are of different political persuasions, I have a great trust in both is character and his abilities... Earlier Friday morning, Rout had said he doubted he would pursue a two-nominee strategy, which might allow both Miller and a white Republican (Rep. Joe Kents name had received some mention) to be appointed from the House. Rout indicated he would make an appointment on Monday. The presence of both a Senate and House member on the PBA is mandated by recent legislation which, though largely unnoticed at the time, was passed by both chambers of the General Assembly and signed into law by Governor Don Sundquist.