THIS MORNING in the auditorium of the Times Mirror Co. in Los Angeles, a group of 34 people will gather. Among them will be a famous actor, a famous opera singer, some of the country's most successful businessmen, foundation directors, fund-raisers, academics, and the national finance chairman of the Reagan campaign.

Some of those present have worked virtually all summer preparing to talk about cultural problems like. how to increase private support for the arts in this country. Nancy Mehta, the former vice president of the 400 Group of the Los Angeles Music Center and the wife of Zubin Mehta, conductor of the New York Philharmonic, hired a researcher to help her locate information on arts funding. Others just started this past week doing homework.

After two months of coast-to-coast phone calls and mailings, the White House Task Force on the Arts and the Humanities in holding its most crucial meeting since its inception. Almost a complete group (missing two members) will assemble for the first time since they originally met on June 15. Charlton Heston (the famous actor) is so-chair of this task force for the arts. The other co-chairs are Hanna Gray, the president of the University of Chicago, who presides over the humanities, and Daniel Terra, the State Department's ambassador-at-large for cultural affairs, represents the government.

There have been few meetings (four to be exact and three of those were regional) and a lot of floundering. Some members have attended one or none of the meetings. In fact, in one recent article in The New York Times, one task force member (who has been attending meetings) inadvertently referred to Arthur Mitchell, the black founder of the Dance Theatre of Harlem and a member of the task force, as Alvin Ailey, the black choreographer who also has his own dance company in New York.

"The timetable is short and it takes a while for these things to get organized, for [task force members] to work their way through to a definition of what they think are the principal questions," said Gray.

"You can't expect a cosmic solution to problems when the group has had only a few meetings," said Franklin Murphy, chairman of the executive committee of the board of the Times Mirror Co. in Los Angeles.

But they have finally come together to decide what will go into their report to the president this fall. And they'll begin by discussing the following issues:

* Possible tax incentives to encourage corporate giving -- including a tax credit plan devised by Terra.

This will be important since the Reagan tax plan, now approved by Congress, not only reduces individuals' taxes but also speeds up the rate at which companies can write off capital investments. Companies end up with less taxable income and therefore less of a tax incentive to donate money.

* Alternative structures for the endowments.

However, it is unlikely that any different structure, like the Corporation for Public Broadcasting model, will be chosen.

* The successful "challenge grant" program, in which a grantee must match every federal dollar received with three dollars from the private sector.

Two issues here. Should the matching ratio be increased to encourage even more private monies? And should the endowments set aside more of their funds for challenge grants?

* Revising the National Council on the Arts.

The task force might change the council, an advisory body to the National Endowment for the Arts, into a voting body.

* The role the president should play in fostering support of the arts.

* The possibility of artists getting tax deductions for the full amount of works donated to museums.

Currently, artists can only deduct the cost of materials that went into the works.

One consensus has apparently been reached: The endowments will not be dismantled. "The endowments look better and better as we look into them more," said task force member Henry Geldzahler, commissioner of the New York City department of cultural affairs. "The wild shots, like the one-word poem, hang in the air a while, but that was an exception." He was referring to the one-word poem "LIGHGHT" by Aram Saroyan, which was not composed on an NEA grant, but appeared in the NEA-sponsored "American Literary Anthology." The NEA paid a fee to every author whose work appeared in the anthology.

The task force probably won't turn the agencies into quasi-governmental corporations either, like the Corporation for Public Broadcasting. "That's pretty well dead," said Geldzahler.

His comments were echoed by most of the other members interviewed. "The corporate model has at least as many problems as the endowment structure," said Theodore Ziolkowski, dean of the graduate school at Princeton University. He has been attending task force meetings in the place of Princeton President William Bowen.

Most task force members feel they shouldn't touch the sticky ground of evaluating programs in the endowments. "What the task force is charged with and what it ought to do is to talk about the course that ought to be set," Gray say a few weeks ago. "I don't think it would be appropriate for this group to try to say in detail what the individual programs would be. I think it ought to speak to the question of whether there ought to be a federal presence in the arts and the humanities."

And on that question, the answer will be yes as far as anyone can tell. The task force, says Gray, "is going in the direction of affirming the value of the structure of the endowments and the system of peer review as kind of fundamental structures. I'll be surprised if it goes in a different way."

The big discussion today will be how to increase corporation and individual funding for the arts and the humanities. Some would rather not get too involved in the tax issue. "I don't think we should get wrapped up in the tax laws," said Ziolkowski.

"We seem to have found that corporation giving is very, very small in relation to individual giving," said Nancy Mehta. "I would suggest we look at individual giving."

Terra -- who wants to tackle tax issues -- agrees. "The real impact on the arts and the humanities will come from the tremendous changes in the tax law, not from the budget cuts," said Terra, who was Reagan's campaign finance chairman, and a supporter of the president's tax cuts. "The budget cuts are minor. I would like to suggest an emergency tax incentive plan that would give individual taxpayers a break in the form of a tax credit."

Terra predicts that 1982 tax reductions to taxpayers now in the $50,000 to $100,000 income group will mean a decline of $81 million in contributions just to arts and humanities groups, just from that income category. (That doesn't include the decline in other philanthropic contributions.) He bases those figures -- and similar figures for other taxpayers from higher income levels -- on figures for philanthropic contributions in 1970 and 1974. Taxpayers got tax reductions in 1971, according to Terra.

This is how the tax credit would work: A person making close to $100,000 gives, on the average, $1,970 in philanthropic contributions. With the tax reductions, Terra figures this person will only give about $1,700. But if he gets a tax credit for giving more, hopefully he'll give more.

The president could play a role in increasing private support for the arts, according to an information report done by the staff of the task force members. They even suggested "Presidential Minutes," like the "Bicentennial Minutes," in which the president would appear briefly on televised spots focusing on different arts organizations. These would not be pleas for money, the task force staff wrote in their report. Ideas like these will probably come up today at the meeting.

Terra has another idea he plans to unveil today -- a private foundation to support the arts and humanities. This would be in addition to the two endowments. "It would be the National Foundation for Cultural Development," he said. "I'm toying with the name. It should have the competence and the professionalism to give outright grants, challenge grants, matching grants, as well as to initiate programs."

Terra said it would take about $20 million $30 million to start up and it would not be an endowment. "I've talked to some of the task force members about it," he said. "Some like it. Some don't."

Task force members have been mulling over ways to revamp the challenge grant program to bring in more private money. Murphy said he thinks challenge grants should be specified on a sliding scale: "You would have to measure the kinds of constituents and financial situation." Arts organizations with poorer constituents would have a lower than three-to-one matching ratio. Those with richer constituents would have a higher ratio. Asked who would make the decisions about which group got what type of challenge grant, Murphy said, "That's what you have a National Council on the Arts and a chairman for."

Said Geldzahler, "We have to negotiate the private sector into supporting the arts. They key is matching grants. We could change two to one matches to three to one matches. That seems perfectly Reaganesque to me."

The task force was first conceived early this spring by New York attorney Barnabas McHenry, now the vice chairman, in the midst of an impending crisis in the arts world which -- partially due to the demonstrations of noted artists -- never quite materialized to the extent feared. The Reagan proposal to slash the arts and humanities endowments in half -- down to $88 million and $85 million respectively -- is now pretty much a thing of the past. The staunch arts supporter, Rep. Sidney Yates (D-Ill.), got an appropriations figure of $157.5 million for the NEA and $144.6 million for the NEH through the House. And the Senate Appropriations Committee voted to fund the NEA at $119.3 million and the NEH at $113.7 million. Eventually a conference committee will have to reconcile the two figures.

The proposed rescissions in current fiscal year 1982 funds, which caused such an outcry, were drastically reduced. About a week ago, both endowments were quietly informed that the rescission proposal for the remaining amount that had expired. So there will be no rescissions.

The endowments still have to cut back. Some officials of the NEA are, privately, subdued and depressed about the future of the endowment. Okay, they may have weathered budget-cut fever well this year, some say ominously, but what about next year? Remembering how transition official Bob Carter told them this winter that OMB director David Stockman originally wanted the endowments abolished, some endowment observers see this year only as a temporary reprieve from worse fates to come.

But the task force, which was also feared by some endowment officials and National Council on the Arts members, appears to be fairly happy with the endowments -- at least as much as they know about it. "There've been a lot of comments very supportive of the endowments," said Edmund Pillsbury, director of the Kimbell Art Museum in Fort Worth, Texas. "That's not to say that they won't have to get along with less money. But there seems to be a consensus that on balance the endowments have done a fairly good job."