Partial flag varieties and preprojective algebras

Christof Geiß[1]; Bernard Leclerc[2]; Jan Schröer[3]

  • [1] Universidad Nacional Autónoma de México Instituto de Matemáticas 04510 México D.F. (México)
  • [2] Université de Caen LMNO UMR 6139 14032 Caen cedex (France)
  • [3] Universität Bonn Mathematisches Institut Beringstr. 1 53115 Bonn (Germany)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 3, page 825-876
  • ISSN: 0373-0956

Abstract

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Let Λ be a preprojective algebra of type A , D , E , and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ -module, and we introduce a mutation operation between complete rigid modules in Sub Q . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to  G .

How to cite

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Geiß, Christof, Leclerc, Bernard, and Schröer, Jan. "Partial flag varieties and preprojective algebras." Annales de l’institut Fourier 58.3 (2008): 825-876. <http://eudml.org/doc/10336>.

@article{Geiß2008,
abstract = {Let $\Lambda $ be a preprojective algebra of type $A, D, E$, and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $\{\rm Sub\,\} Q$ for $Q$ an injective $\Lambda $-module, and we introduce a mutation operation between complete rigid modules in $\{\rm Sub\,\} Q$. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$.},
affiliation = {Universidad Nacional Autónoma de México Instituto de Matemáticas 04510 México D.F. (México); Université de Caen LMNO UMR 6139 14032 Caen cedex (France); Universität Bonn Mathematisches Institut Beringstr. 1 53115 Bonn (Germany)},
author = {Geiß, Christof, Leclerc, Bernard, Schröer, Jan},
journal = {Annales de l’institut Fourier},
keywords = {Flag variety; preprojective algebra; Frobenius category; rigid module; mutation; cluster algebra; semicanonical basis; partial flag varieties; preprojective algebras; semicanonical bases; parabolic subgroups; semisimple algebraic groups; injective modules; quadrics; rigid modules; cluster algebras; Grassmannians},
language = {eng},
number = {3},
pages = {825-876},
publisher = {Association des Annales de l’institut Fourier},
title = {Partial flag varieties and preprojective algebras},
url = {http://eudml.org/doc/10336},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Geiß, Christof
AU - Leclerc, Bernard
AU - Schröer, Jan
TI - Partial flag varieties and preprojective algebras
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 3
SP - 825
EP - 876
AB - Let $\Lambda $ be a preprojective algebra of type $A, D, E$, and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories ${\rm Sub\,} Q$ for $Q$ an injective $\Lambda $-module, and we introduce a mutation operation between complete rigid modules in ${\rm Sub\,} Q$. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$.
LA - eng
KW - Flag variety; preprojective algebra; Frobenius category; rigid module; mutation; cluster algebra; semicanonical basis; partial flag varieties; preprojective algebras; semicanonical bases; parabolic subgroups; semisimple algebraic groups; injective modules; quadrics; rigid modules; cluster algebras; Grassmannians
UR - http://eudml.org/doc/10336
ER -

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