We present a uniform construction of tensor products of one-column
Kirillov-Reshetikhin (KR) crystals in all untwisted affine types, which uses a
generalization of the Lakshmibai-Seshadri paths (in the theory of the
Littelmann path model). This generalization is based on the graph on parabolic
cosets of a Weyl group known as the parabolic quantum Bruhat graph. A related
model is the so-called quantum alcove model. The proof is based on two lifts of
the parabolic quantum Bruhat graph: to the Bruhat order on the affine Weyl
group and to Littelmann's poset on level-zero weights. Our construction leads
to a simple calculation of the energy function. It also implies the equality
between a Macdonald polynomial specialized at t=0 and the graded character of a
tensor product of KR modules.Comment: 10 pages, 1 figur
