(What follows is an epitome of the comments in Nagy 2012:49–51.) The narrative here at O.24.036–097 is pervaded by references to the hero cult of Achilles. I offer here a brief inventory of some of these references:
—O.24.036, ὄλβιε Πηλέος υἱέ, θεοῖσ’ ἐπιείκελ’ Ἀχιλλεῦ ‘O you olbios son of Peleus, godlike Achilles’. So, Agamemnon here addresses Achilles as olbios, which would mean ‘fortunate’ on the surface. Beneath the surface, however, olbios here can be interpreted as ‘blessed’, referring to the sacred status of a cult hero: see the comment at O.19.107–114, with special reference to uses of olbios in the sense of ‘blessed’, as at verse 172 of the Hesiodic Works and Days.
—O.037–039, ἀμφὶ δέ σ’ ἄλλοι | κτείνοντο Τρώων καὶ Ἀχαιῶν υἷες ἄριστοι | μαρνάμενοι περὶ σεῖο ‘On all sides of you [= your corpse], the rest of them | were being slaughtered, sons of both Trojans and Achaeans, the best, | as they were fighting over you [= your corpse]’. The Achaeans and the Trojans are battling here over the possession of the corpse of Achilles. The mentality of needing to possess the body of the dead hero, whether he was a friend or an enemy in life, is typical of hero cults, in that the corpse of the cult hero was viewed as a talisman of fertility and prosperity for the community that gained possession of the hero’s body. Details in PH 32, 178; also Nagy 2006§97.
—O.24.039–40, σὺ δ’ ἐν στροφάλιγγι κονίης | κεῖσο μέγας μεγαλωστί ‘There you were, lying in a swirl of dust. | You lay there so huge in all your hugeness’. The corpse of Achilles is described here as larger than life. This wording applies to Achilles also at I.18.026–027, where he stages himself as a corpse in mourning the death of Patroklos and where he is mourned by Thetis as if he were already a corpse: see the comment at I.018.070–071 (see also BA 113, especially with reference to I.18.071). At I.16.775–776, cognate wording applies to the corpse of the hero Kebriones. The corpse of Achilles is described as nine cubits long in the Alexandra of Lycophron (860). As we see from lore preserved in the historical period about cult heroes, they were conventionally pictured as far larger in death than they had been in life. Among the most striking examples is the corpse of Orestes as cult hero, described in Herodotus 1.68.
—O.24.059, περὶ δ’ ἄμβροτα εἵματα ἕσσαν ‘They [= the Nereids] dressed you [= your corpse] in immortalizing clothes’. At the funeral of Achilles, his divine mother and her sister Nereids dress the hero’s corpse in ‘immortalizing’ clothes. On the vital importance of understanding ambrotos as ‘immortalizing’ as well as ‘immortal’, see the comments at I.16.670 and I.16.680; details in GMP 141.
—O.24.073–077. After the cremation of the corpse of Achilles, his bones and those of the already cremated corpse of Patroklos are placed into a golden jar that had been given by the god Dionysus to the goddess Thetis. This jar, as we know from the comparative evidence of other poetic references (especially Stesichorus PMG 234), is a sign of the hero’s immortalization after death. See BA 209; also Dué 2001.
—O.24.085–086. After the making of the tumulus which will be the tomb shared by Achilles and Patroklos, O.24.080–084, funeral games are held in honor of Achilles. The details of this description match closely the details we can gather from historical evidence about athletic contests held in honor of cult heroes. Details in BA 116–117.
—O.24.091. The athletic contests at the funeral games of Achilles and the prizes to be won in these contests are instituted for the purpose of compensating for his death, and, in this verse, such an act of compensation is expressed by way of the prepositional phrase epi soi (ἐπὶ σοί), which can be translated roughly as ‘in your honor’. As we can see clearly from a variety of prose sources, the syntactical construct combining the preposition epi with the dative case of a given hero’s name refers to the cult of that hero. (Details in PH 121.) Perhaps the most striking example is this entry in the dictionary attributed to Hesychius: ‘balletus: a festival event at Athens, held in honor of [epi plus object in dative case] Demophon son of Keleos’ (Βαλλητύς· ἑορτὴ Ἀθήνησιν, ἐπὶ Δημοφῶντι τῷ Κελεοῦ ἀγομένη).