After lunch on March 1, David Solomon was standing at his desk in his 41st-floor office at Goldman Sachs, high above the Hudson River, answering e-mails and talking on his telephone headset. For the previous 15 months, Solomon had been locked in a competition with Harvey Schwartz, with whom he served as co-chief operating officer at Goldman, for one of the most coveted positions on Wall Street. One of them would be picked to succeed Lloyd Blankfein, the bank’s chairman and C.E.O., whenever he decided the time had come to step down.