Adrian Peterson's hearing begins

The NFL Players Association has submitted a recording and transcript of a conversation between Adrian Peterson and NFL executive Troy Vincent to Harold Henderson, the man hearing the Minnesota Vikings running back's appeal of his indefinite suspension.

Peterson's appeal hearing wrapped up for the day by Tuesday afternoon. Peterson did not testify, but Harold Henderson wants Vincent to testify, a source told ESPN NFL Insider Adam Schefter.

ESPN's Andrew Brandt reports a decision on the appeal is expected in a week.If Peterson loses his appeal, it is possible that the entire issue could end up in court, with Peterson and the NFLPA claiming they couldn't get fair arbitration after asking that Henderson recuse himself.

George Atallah, executive director of external affairs for the NFLPA, talked about the recording Tuesday on ESPN Radio's "Mike and Mike" program.

"We believe [Vincent] told him [Peterson] something to the effect of his time on the commissioner's list would be contributed to time served. We'll find out," he said.

"The two issues at play here ... first, what did Troy Vincent actually say ... the good news there is we have a recording of that conversation, so it's pretty indisputable what that conversation was about," Atallah added. "And the second most critical thing is ... is Harold Henderson going to allow or force Troy to be cross examined about what he said. And that's something that we believe is important as part of the appeals hearing that Adrian Peterson is going to go through starting today. And we hope that is the case. That is the only thing that we would find to be fair."

In that conversation, sources told ESPN that Vincent, the NFL's executive vice president for football operations, allegedly tells Peterson he will get time served plus a two-game suspension if Peterson attends a disciplinary hearing with NFL commissioner Roger Goodell on Nov. 14.

Peterson taped the conversation with Vincent in mid-November in Texas, which is a "one-party consent state." That means a person can tape a conversation and is not legally bound to inform the person to whom they are speaking that the conversation is being recorded.

Peterson declined to attend that hearing with Goodell. At the time, USA Today Sports reported Peterson told the league he would meet with Goodell to discuss potential discipline, but would not attend the Nov. 14 hearing because there were too many unanswered questions about the process.

Four days later, on Nov. 18, the NFL suspended Peterson without pay for at least the remainder of the 2014 season for violating the league's personal conduct policy. He will not be eligible to apply for reinstatement until April 15, 2015. On Nov. 4, Peterson pleaded no contest to misdemeanor reckless assault in Texas for injuries he caused to his 4-year-old son with a wooden switch.

Peterson immediately appealed the suspension.

Vincent, who was in Washington, D.C., to testify at a Congressional hearing on domestic violence, is not expected to testify at Peterson's hearing. The NFLPA has asked the NFL to force Vincent to testify as a "central witness" in the case.

The validity of Vincent's offer and whether he had the authority to make such an offer is unknown, but is expected to be questioned during Peterson's hearing.

Henderson, formerly the NFL's executive vice president for labor relations, was appointed by Goodell to hear Peterson's appeal, after the union asked for an independent hearing officer.