The A2 Bailey chain of Andrews, Schilling and the author is extended to a four-parameter A2 Bailey tree. As main application of this tree, we prove the Kanade-Russell conjecture for a three-parameter family of Rogers-Ramanujan-type identities related to the principal characters of the affine Lie algebra A2(1)
Nearby in the stack
. Combined with known
q
-series results, this further implies an
A2(1)
-analogue of the celebrated Andrews-Gordon
q
-series identities. We also use the
A2
Bailey tree to prove a Rogers-Selberg-type identity for the characters of the principal subspaces of
A2(1)
indexed by arbitrary level-
k
dominant integral weights
λ
. This generalises a result of Feigin, Feigin, Jimbo, Miwa and Mukhin for