Rich's poem is a retelling of the Orpheus myth. In the myth, Orpheus, a great musician, loves Eurydice; when she dies, he descends into the underworld to seek her spirit. Hades agrees to allow Orpheus to take Eurydice back to Earth but only if he leads her and does not look back to see if she is following. At the last moment, Orpheus does look back, and Eurydice is dragged back to hell. Heartbroken, Orpheus dies.
In the myth, Eurydice is a kind of muse. Orpheus's love for her is what motivates her actions; Eurydice herself has no agency, except to follow. Her doom is sealed not through any action she has taken but through Orpheus's weakness. In the poem, the dreamer imagines herself as the agent of the process, the cause of Orpheus's death. She is a woman of "certain powers" which are "severely limited" by "authorities"—powers "she must not use" in order to complete a "mission" that, if completed, will "leave her intact."
It's clear that these "powers" are the powers of the poet; if we understand the dream woman to be Eurydice, then her poetic powers are subordinate to Orpheus's. Even though she can see "through the mayhem" of hell, she cannot be her own guide. In this way the "woman" is not only shown to be stronger than Orpheus but also able to subdue her own ego in order to fulfill her role; she is one who comprehends, in her own "lucidity," her position as both muse and artist.