It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. In particular, certain Demazure crystals are isomorphic as classical crystals to tensor products of Kirillov-Reshetikhin crystals via a canonically chosen isomorphism. Here we show that this isomorphism intertwines the natural affine grading on Demazure crystals with a combinatorially defined energy function. As a consequence, we obtain a formula of the Demazure character in terms of the energy function, which has applications to Macdonald polynomials and $q$-deformed Whittaker functions.
@article{10_37236_2184,
author = {Anne Schilling and Peter Tingley},
title = {Demazure crystals, {Kirillov-Reshetikhin} crystals, and the energy function},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {2},
doi = {10.37236/2184},
zbl = {1247.81218},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2184/}
}
TY - JOUR
AU - Anne Schilling
AU - Peter Tingley
TI - Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2184/
DO - 10.37236/2184
ID - 10_37236_2184
ER -
%0 Journal Article
%A Anne Schilling
%A Peter Tingley
%T Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2184/
%R 10.37236/2184
%F 10_37236_2184
Anne Schilling; Peter Tingley. Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2184
