UNITED NATIONS — At the baronial Morgan Library in Midtown Manhattan the other night, President Mahmoud Abbas, the Palestinian leader, stood quietly along the edge of a diplomatic reception, avoiding the animated gossip and flowing Champagne.

Only when the host noted that Mr. Abbas was in the room, and expressed hope that his quest for Palestinian membership in the United Nations would produce real sovereignty, did the crowd take notice.

For decades, the defiant, charismatic and unpredictable Yasir Arafat, always in military uniform, needed no introduction. Seven years after Mr. Arafat’s death, Mr. Abbas, a gray man of sober suits and sensible shoes, may now be slowly emerging from his shadow.

In bringing his cause to the United Nations despite intense American pressure, Mr. Abbas has captivated the annual General Assembly gathering, bolstered the flagging devotion of his people and even cornered his rivals in Hamas. The question is whether this moment of unparalleled prestige for the Palestinian leader will produce concrete results or a new and more dangerous set of risks.