Journal of Combinatorics

Volume 4 (2013)

Number 4

Intrinsic energy is a loop Schur function

Pages: 387 – 401



Thomas Lam (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Pavlo Pylyavskyy (Department of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)


We give an explicit subtraction-free formula for the energy function in tensor products of Kirillov-Reshetikhin crystals for symmetric powers of the standard representation of ${U_q'({\mathfrak{\hat{sl_n}}})}$. The energy function is shown to be the tropicalization of a stretched staircase shape loop Schur function.

The latter were introduced by the authors in the study of total positivity in loop groups.

Published 27 December 2013