A new tri-governmental board created to advise Salt Lake County's Salt Palace and Fine Arts Division may begin holding meetings next week despite the Salt Lake City Council's inability to agree on its board representatives.

The city also has not paid its portion of the division's operations subsidy, which is being jointly underwritten by the county, city and state. And if some assurance of city payment doesn't come soon, the division could face budgeting difficulties, said county commission Chairman Bart Barker.An interlocal agreement signed by the three governments in June calls for them to jointly subsidize the operations of the county's fine arts facilities - Symphony Hall, the Capitol Theater and the Salt Lake Arts Center - at a maximum of $1.275 million annually.

For 1988 each government entity has agreed to contribute $335,000 to the subsidy. The county and state have already paid their portions.

The agreement also allows each government to appoint three representatives to a nine-member board that will advise the Salt Palace and Fine Arts Division on policy.

While the county and state have confirmed board representatives, the city has been unable to settle on its members. The City Council rejected Mayor Palmer DePaulis' three nominees last month.

DePaulis has designated Nancy Boskoff, the Salt Lake City Arts Council director, as his liaison to the board. The city has also asked that the board not conduct business until its representatives are named, but it gave no indication when the appointments will come.

The initial meeting of the new advisory board is scheduled for next week, and if the six county and state representatives are present, the board would have a quorum even if the city's appointees have not been named.

County officials are reluctant to delay the meeting despite the city's lack of board representation. A former advisory board, with members appointed only by the county, has been dissolved, and the new board needs to begin conducting business so it can review the division's budget for the new fiscal year, beginning Jan. 1.