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

David Hernandez; Bernard Leclerc

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 5, page 1113-1159
- ISSN: 1435-9855

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topHernandez, 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 -

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