ANALYSIS: The death of the Rev. Jesse Jackson produced the unexpected: a public split between two of Chicago’s most prominent Democratic figures. The day after Jackson died on Feb. 17, his son, Jesse Jr., appeared with other family members outside the civil rights icon’s Chicago home. Mr. Jackson, a former congressman now running to reclaim Illinois’ 2nd District House seat, eulogized his 84-year-old father. And he set the rules for a series of upcoming memorials, saying the services should be