He is the Third person of the Trinity. The right hand is held in Hamsaya used to denote Holy or Blessing. Holy is the 'Numinous' the mysterious quality of the divine (Is 2:2ff).
"The son came down from heaven: by the power of the Holy Spirit" (Apostle Creed). The left hand is held in Tripataka Symbolising raising flame, here used for the spirit. Spirit in the scriptures is conceived as dynamic entity by which God accomplished His ends. The conception of Jesus is attributed to the Holy Spirit (Mt 1:18.20).
The Holy Spirit enlightens man (1 Cor. 2:10-16).
We believe in Holy Spirit, the Lord, the giver of life, who proceeds from the Father and the Son. With the Father and the Son he is worshipped and glorified (AC). The left hand is kept near the heart which is supposed to be the seat of love. life, dynamism, affection, unity etc.