Each of the brothers symbolize something; Arjuna symbolizes Manipura

Arjuna is the star of the Gita, and is sybolic of the 3rd chakra, Manipura, or the "jewel city".  Arjuna is the brother who symbolizes the individual self, the warrior, the austere and disciplined soul.

Some factoids about Arjuna and Manipura:
  •  Manipura is situatued at the navel, and associated with digestion both of food and with assimilation of ideas.
  • Manipurna is associated with the fire element, the visua sense, and the anus.
  • "Ram" is the bija mantra of the Manipura chakra.
  • This chakra, in balance, promotes austerity, tapas, self discipline, personal growth, and forbearance, or Titikisha.
    • In the Mahabarata, Arjuna, the emobodiment of Manipura, hid out as a palace eunich among all the court ladies.  His austere nature never wavered.
  • This chackra, out of balance, symbolizes the kleshas is the propogator of fear, anxiety, negative actions rooted in ignorance, greed, and misplaced loyalty.
    • Karna, the Kaurava brother, is the character who symbolizes the negative counterpart of Arjuna and the embodiment of imbalanced Manipura.
  • Manipura chakra has 10 petals
    • dam - shame
    • dham - slander or fickleness
    • nam - jealousy 
    • tam - desire
    • tham - laziness, drowsiness
    • dam - dullness, worldliness
    • dham - sadness, despondency
    • nam - ignorance, delusion
    • pam - aversion, disgust
    • pham - fear