A cluster algebra approach to $q$-characters of Kirillov–Reshetikhin modules

Hernandez, David, and Leclerc, Bernard. "A cluster algebra approach to $q$-characters of Kirillov–Reshetikhin modules." Journal of the European Mathematical Society 018.5 (2016): 1113-1159. <http://eudml.org/doc/277643>.

@article{Hernandez2016,
abstract = {We describe a cluster algebra algorithm for calculating $q$-characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra $U_q(\widehat\{\mathfrak \{g\}\})$. This yields a geometric $q$-character formula for tensor products of Kirillov–Reshetikhin modules. When $\mathfrak \{g\}$ is of type $A, D, E$, this formula extends Nakajima’s formula for $q$-characters of standard modules in terms of homology of graded quiver varieties.},
author = {Hernandez, David, Leclerc, Bernard},
journal = {Journal of the European Mathematical Society},
keywords = {quantum affine algebra; cluster algebras; $q$-characters; Kirillov–Reshetikhin modules; geometric character formula; quantum affine algebra; cluster algebras; -characters; Kirillov-Reshetikhin modules; geometric character formula},
language = {eng},
number = {5},
pages = {1113-1159},
publisher = {European Mathematical Society Publishing House},
title = {A cluster algebra approach to $q$-characters of Kirillov–Reshetikhin modules},
url = {http://eudml.org/doc/277643},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Hernandez, David
AU - Leclerc, Bernard
TI - A cluster algebra approach to $q$-characters of Kirillov–Reshetikhin modules
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 5
SP - 1113
EP - 1159
AB - We describe a cluster algebra algorithm for calculating $q$-characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra $U_q(\widehat{\mathfrak {g}})$. This yields a geometric $q$-character formula for tensor products of Kirillov–Reshetikhin modules. When $\mathfrak {g}$ is of type $A, D, E$, this formula extends Nakajima’s formula for $q$-characters of standard modules in terms of homology of graded quiver varieties.
LA - eng
KW - quantum affine algebra; cluster algebras; $q$-characters; Kirillov–Reshetikhin modules; geometric character formula; quantum affine algebra; cluster algebras; -characters; Kirillov-Reshetikhin modules; geometric character formula
UR - http://eudml.org/doc/277643
ER -