When the Kirov Ballet came to New York in 2002, it pulled into the Met like the greatest show on earth. The company brought a this-is-how-it’s-done Don Quixote and a Swan Lake with the lovely, dusty sheen of old velvet in stone castles. Its La Bayadère, like The Sleeping Beauty brought here in 1999, was an experiment in history retrieved, a ballet rebuilt from notated texts, and though not wholly satisfying as a work of art, it was a restoration with many fascinations. And then there were three splendid performances of George Balanchine’s Jewels, which arrived with a newly designed set, still minimalist, but less the static parure that was the design for decades at New York City Ballet and more a swirling star shower from above, as if the vaults of heaven had opened.

When I think of the Kirov, I think of vaults. It’s not just the rich history of this company, which ...