A.T. Robertson Commentary Galatians 2:9

"and when they perceived the grace that was given unto me, James and Cephas and John, they who were reputed to be pillars, gave to me and Barnabas the right hands of fellowship, that we should go unto the Gentiles, and they unto the circumcision;" — Galatians 2:9 (ASV)

They who were reputed to be pillars (ο δοκουντες στυλο εινα). They had that reputation (δοκουντες) and Paul accepts them as such. Στυλο, old word for pillars, columns, as of fire (Revelation 10:1). So of the church (1 Timothy 3:15). These were the Pillar Apostles.

Gave to me and Barnabas the right hands of fellowship (δεξιας εδωκαν εμο κα Βαρναβα κοινωνιας). Dramatic and concluding act of the pact for cooperation and coordinate, independent spheres of activity. The compromisers and the Judaizers were brushed to one side when these five men shook hands as equals in the work of Christ's Kingdom.