X=M for symmetric powers
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X=M for symmetric powers

  • Author(s): Schilling, Anne
  • Shimozono, Mark
  • et al.

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The X=M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac--Moody algebra. In this paper we prove the X=M conjecture for tensor products of Kirillov--Reshetikhin crystals B^{1,s} associated to symmetric powers for all nonexceptional affine algebras.

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