The word "supergroup" is overused hyperbole, but it's difficult to avoid when describing Rez Abbasi's Invocation.

Pianist Vijay Iyer and alto saxophonist Rudresh Mahanthappa perennially earn jazz music accolades for the instruments they play and the records they release under their own names. To have two such renowned band leaders and dynamic stylists retain membership in someone else's ensemble, while fostering the sort of affinity that comes with ongoing experience together, is a rare treat.

Rarer still is the chance to hear the entire band in concert, playing material so new it has yet to be released. But that will be the situation on Thursday at the Walker Art Center in Minneapolis, when Invocation performs songs exclusively from its third album, recorded just a few weeks ago and yet to be mixed and mastered.

Abbasi, a Pakastani-born guitarist and composer and the leader of Invocation, said, "This new record is the third part of a trilogy I have been working out."

The first Invocation album, "Things to Come," from 2009, blended traditional North Indian music with jazz. "I wanted to bring my wife [Indian-Canadian vocalist Kiran Ahluwalia] from the world of raga into more improvised music and open her up," Abbasi said.

"Suno Suno," recorded in 2012, mixed Abbasi's love of the Sufi devotional music, known as qawwali, with jazz.

For the new material that will be performed at the Walker, Abbasi again taps his South Asian heritage, plying jazz improvisation within the South Indian classical genre known as Carnatic music.

Fittingly, the inspiration for these new songs stems in part from Abbasi's collaboration with Minneapolis-based Ragamala Dance Company, beginning with a project at the Walker in 2014 when the guitarist was a member of Mahanthappa's band.

"I learned a lot about the Carnatic aspect performing with Rudresh and [traditional Indian saxophonist] Kadri Gopalnath — playing within the context of the music instead of just studying it," Abbasi said. "But seeing the dancers dance the rhythmic ideas and having to internalize them in the music, that's where it's at."

It is tempting to think Mahanthappa and Iyer are loyal to Invocation at least partly due to their empathy with Abbasi's South Asian roots — both are sons of Indian immigrants. But Abbasi is a formidable guitarist and a challenging composer, writing material that walks the line between the mathematic precision and discipline of South Asian music and the more freewheeling creativity of jazz.

"I think the new songs are great because they give us more space to push on them and shape them as we interact together," Iyer said. "The way improvisation functions is more central than in the first two records. So even the places that are carefully orchestrated, with the cello [from band member Elizabeth Means] and the beautiful colors and counterpoint, it can still be cracked wide open for the band to create a path through the music."

He added: "There are a lot of grooves we can dig into. But it is not so much about soloing or burning, but creating radiance as a pulse when we communicate."

A mini supergroup?

As an added bonus, the Invocation performance at the Walker will be preceded by a short set from Mahanthappa's Indo-Pak Coalition, the saxophonist's trio with Abbasi and percussionist Dan Weiss, who also plays in Invocation and has released highly praised albums under his own name.

"First of all, Rez is a ridiculous guitarist with incredible technique who can manipulate," Mahanthappa said. "He has so many different guitars, pays great attention to detail and knows what he is trying to find in the music, so the sonic blends he gets are unbelievable."

Indeed, it was after watching Abbasi play one night that Mahanthappa said he was inspired to resurrect the Indo-Pak Coalition after the first incarnation was hijacked by a former bandmember.

'Hard band to get together'

It is a crazy, fruitful time in Abbasi's career. In the past month alone, he has mixed and mastered a recording from his electric band, Junction; gone into the studio to record the Invocation album, and gone out on tour with his third ensemble, Rock, which plays old fusion jazz songs on acoustic instruments.

Now comes the Walker performance.

Iyer just released a disc of duets with trumpeter Leo Wadada Smith and is curating and playing a monthlong performance residency at the Metropolitan Museum of Art in New York City. Mahanthappa has a similar slew of projects in various stages of development.

"Believe me, this is a hard band to get together," Abbasi said with a laugh. "We're lucky to have found a time."

The audience is likely to feel the same way on Thursday night.

Britt Robson is a Twin Cities-based writer.