AMNA NAWAZ: The Supreme Court heard arguments today in a death row case from Oklahoma that's garnered national attention.

Justices looked at whether the due process rights of a death row inmate named Richard Glossip were violated when the state suppressed information about its star witness who committed the murder.

An Oklahoma court of criminal appeals has denied Glossip's appeal for a retrial.

Our Oklahoma communities correspondent, Adam Kemp, has been following this case and joins us now.

Adam, good to see you here.

ADAM KEMP: Nice to see you.

AMNA NAWAZ: So, remind us now, who exactly is Richard Glossip and why is this case significant?

ADAM KEMP: Yes, Richard Glossip was convicted and sentenced to death in 1998 for the murder of Barry Van Treese.

His case has been has had many ongoing developments over the years.

In 26 years, he's faced nine different execution dates, he's eaten three last meals.

And, today, he gets to go before the Supreme Court to have his case heard.

It's also unique, because Oklahoma's attorney general, Gentner Drummond, a Republican, is really leading the effort here to have Glossip get a new trial.

He has been a pretty staunch advocate that Glossip's due process was denied and that it should go to retrial.

It's also unique that the Supreme Court is hearing a death row case at all.

It's been a couple of years since they have actually taken on any arguments in that regard.

AMNA NAWAZ: That is really unique.

And you had a chance to be in there today in the court as oral arguments were unfolding.

So tell us a little bit about what exactly Supreme Court justices are weighing here, what they're considering.

ADAM KEMP: Yes.

Yes, the Supreme Court's considering two things, one, whether Glossip's due process was denied.

There's a lot of evidence that shows that Sneed, the state's star witness and the person who actually committed the murder of Barry Van Treese, lied under oath about his treatment for mental health issues.

He's also the one that pointed the finger at Glossip, saying that he orchestrated the whole entire thing.

There was also a second question about whether the Supreme Court has jurisdiction to overturn a state Supreme Court ruling.

In this case, it's more about whether the attorney general, Drummond, has the right to get a retrial when he asks for it from the state court.

AMNA NAWAZ: Yes, I mean, that's so interesting.

How did the justices seem to be grappling with that issue when you heard them?

ADAM KEMP: Yes, it seemed pretty split up along party lines.

The conservative justices, Alito and Thomas, really hammered home and questioned whether there would be a big impact from a jury knowing this lie in a trial, whereas the liberal bench questioned, why would the Supreme Court not have jurisdiction over the state court?

And then worth pointing out as well that Justice Gorsuch was recused from this hearing because he had previously served on the 10th Circuit for a Glossip hearing.

It kind of seems like it might come down to Justices Kavanaugh and Justices Barrett to maybe make the -- ultimately the deciding decision here.

AMNA NAWAZ: So does the impact of a decision here go beyond Richard Glossip?

I mean, could it impact other death row cases?

ADAM KEMP: Yes, we will get that decision in June.

Right now, it's kind of up in the air.

We don't really know what the impact could be.

I did talk to some death penalty experts just about death penalty as a whole in the U.S. right now.

And they believe that you're going to see more cases like this, that more people are going to challenge not the - - whether a death penalty is right or wrong, but whether or not people are getting the due process when they go through this.

AMNA NAWAZ: Fascinating, fascinating story.

Great reporting by our Oklahoma communities correspondent, Adam Kemp.

Adam, great to have you here.

Thank you.

ADAM KEMP: Thank you.