The Jets have hired Seahawks VP of Football Administration John Idzik as their General Manager. Idzik's main role with the Seahawks was as their salary cap manager; and according to his now obsolete Seahawks website bio, "Idzik oversees player negotiations, the team's compliance with the NFL salary cap, player personnel transactions, all football operations budgets, staff and team contracts, team travel and most aspects of the day-to-day football operations while also remaining active in player evaluations. In addition, he serves as the club's primary liaison to the NFL Office and represents the club at League meetings."
Idzik graduated from Dartmouth magna cum laude with a degree in mathematics and is the son of a former NFL coach. He also played receiver at Dartmouth and coached at Duke and in Europe, so he's been around football his whole life. The Seahawks, of late - possibly to help build his resume out - had sent him on the road scouting players as well, and from what I gather, Idzik was party to a good amount of coaching staff/scouting staff meetings and film sessions. This versatility, both as a cap specialist and as an experienced personnel man, makes him an obvious choice as a GM, so I think the Jets got a good one here.
Idzik has prior stints in NFL front offices with both the Cardinals and Bucs, serving in different roles as a Senior Director of Football Operations for the Cardinals, and prior to that, as a Pro Personnel Assistant, Director of Football Administration, and Assistant General Manager for the Bucs. The Seahawks lose a key member of their front office with this hire, and the main figure behind Seattle's excellently-structured and forward looking salary cap.
As for a possible replacement for Idzik, Jason La Canfora notes that Seattle fans should look for Seahawks to contact former Denver GM Brian Xanders; the 41-year old Xanders was the GM for the Denver Broncos from 2009-2012. His wikipedia page literally looks like an uploaded resume, so you can check that out here. Xanders never had final say on personnel in Denver though, first serving under Mike Shanahan, then Josh McDaniels, then John Elway, so I don't know how much credit or blame can really be assigned, but it's reasonable to assume he had a huge part in building the draft board and 'setting the table for the buffett,' as we'll say with John Schneider here (Pete Carroll has final say on every pick).
All I know is that Denver hit on a lot of players in Xanders' time there in 2010 and 2011. Starters produced from the 2010 draft were, according to the Denver Post, "Demaryius Thomas, Tim Tebow, Zane Beadles, Eric Decker, J.D. Walton and Perrish Cox. In 2011, Von Miller became the NFL defensive rookie of the year and Orlando Franklin was a 16-game starter. Safeties Rahim Moore and Quinton Carter were also starters."
I haven't seen other names yet mentioned, but if you see any, we'll add those to the list.