Objection 1. It would seem that it is not proper to Christ to sit at the right hand of the Father, because the Apostle says (Ephesians 2:4-6): "God... hath raised us up together, and hath made us sit together in the heavenly places through Christ Jesus." But to be raised up is not proper to Christ. Therefore for like reason neither is it proper to Him to sit "on the right hand" of God "on high" (Hebrews 1:3).
Objection 2. Further, as Augustine says (De Symb. i): "For Christ to sit at the right hand of the Father, is to dwell in His beatitude." But many more share in this. Therefore it does not appear to be proper to Christ to sit at the right hand of the Father.
Objection 3. Further, Christ Himself says (Apocalypse 3:21): "To him that shall overcome, I will give to sit with Me in My throne: as I also have overcome, and am set down with My Father in His throne." But it is by sitting on His Father's throne that Christ is seated at His right hand. Therefore others who overcome likewise, sit at the Father's right hand.
Objection 4. Further, the Lord says (Matthew 20:23): "To sit on My right or left hand, is not Mine to give to you, but to them for whom it is prepared by My Father." But no purpose would be served by saying this, unless it was prepared for some. Consequently, to sit at the right hand is not proper to Christ.
On the contrary, It is written (Hebrews 1:13): "To which of the angels said He at any time: Sit thou on My right hand, i.e. 'in My mightier gifts,'" or "'as my equal in the Godhead'"? [The comment is from the gloss of Peter Lombard] as if to answer: "To none." But angels are higher than other creatures. Therefore, much less does it belong to anyone save Christ to sit at the Father's right hand.
I answer that, As stated above (Article 3), Christ is said to sit at the Father's right hand inasmuch as He is on equality with the Father in respect of His Divine Nature, while in respect of His humanity, He excels all creatures in the possession of Divine gifts. But each of these belongs exclusively to Christ. Consequently, it belongs to no one else, angel or man, but to Christ alone, to sit at the right hand of the Father.
Reply to Objection 1. Since Christ is our Head, then what was bestowed on Christ is bestowed on us through Him. And on this account, since He is already raised up, the Apostle says that God has, so to speak, "raised us up together with Him," still we ourselves are not raised up yet, but are to be raised up, according to Romans 8:11: "He who raised up Jesus from the dead, shall quicken also your mortal bodies": and after the same manner of speech the Apostle adds that "He has made us to sit together with Him, in the heavenly places"; namely, for the very reason that Christ our Head sits there.
Reply to Objection 2. Since the right hand is the Divine beatitude, then "to sit on the right hand" does not mean simply to be in beatitude, but to possess beatitude with a kind of dominative power, as a property and part of one's nature. This belongs to Christ alone, and to no other creature. Yet it can be said that every saint in bliss is placed on God's right hand; hence it is written (Matthew 25:33): "He shall set the sheep on His right hand."
Reply to Objection 3. By the "throne" is meant the judiciary power which Christ has from the Father: and in this sense He is said "to sit in the Father's throne." But other saints have it from Christ; and in this respect they are said "to sit on Christ's throne"; according to Matthew 19:28: "You also shall sit upon twelve seats, judging the twelve tribes of Israel."
Reply to Objection 4. As Chrysostom says (Hom. lxv in Matth.), "that place," to wit, sitting at the right hand, "is closed not only to all men, but likewise to angels: for, Paul declares it to be the prerogative of Christ, saying: 'To which of the angels said He at any time: Sit on My right hand?'" Our Lord therefore "replied not as though some were going to sit there one day, but condescending to the supplication of the questioners; since more than others they sought this one thing alone, to stand nigh to Him." Still it can be said that the sons of Zebedee sought for higher excellence in sharing His judiciary power; hence they did not ask to sit on the Father's right hand or left, but on Christ's.
Source: Summa Theologica (New Advent)