what do the mermaids symbolize?

Prufrock immediately switches his attention to the mermaids "singing, each to each" (124) - the society of women who ignore him. The elusive images perhaps have more cohesion than on first glance:

I have seen them riding seaward on the waves

Combing the white hair of the waves blown back

When the wind blows the water white and black.

(126-128)

Prufrock has just wondered "Shall I part my hair behind?" (122), and previously he has agonized over his bald spot, turned his keen eye to the women's arms "downed with light brown hair!" (64), and agonized over eating a fuzzy peach. Mermaids are conventionally depicted combing their hair with a mirror, so as symbols of vanity and lush beauty - "wreathed with seaweed red and brown" (130), they possess even more artificial hair - they threaten Prufrock (whose thinning hair is perhaps now a salt-and-pepper mixture of "white and black" and no longer "red and brown").