Lakshmibai-Seshadri paths of level-zero weight shape and one-dimensional   sums associated to level-zero fundamental representations
  We give interpretations of energy functions and (classically restricted) one-dimensional sums associated to tensor products of level-zero fundamental representations of quantum affine algebras in terms of Lakshmibai-Seshadri paths of level-zero weight shape. 
Satoshi Naito and Daisuke Sagaki