Tous nos rayons

Déjà client ? Identifiez-vous

Mot de passe oublié ?

Nouveau client ?

CRÉER VOTRE COMPTE
Representation of Quantum Algebras and Combinatorics of Young Tableaux
Ajouter à une liste

Librairie Eyrolles - Paris 5e
Indisponible

Representation of Quantum Algebras and Combinatorics of Young Tableaux

Representation of Quantum Algebras and Combinatorics of Young Tableaux

University Lecture Series - volume 26

Susumu Ariki

158 pages, parution le 09/04/2003

Résumé

This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups.

Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras.

The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type A (1){r-1} as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux.

The second goal of this book is to explain the proof of the (generalized) Lascoux-Leclerc-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type.

The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, and related fields.

Contents

  • Introduction
  • The Serre relations
  • Kac-Moody Lie algebras
  • Crystal bases of $U_v$-modules
  • The tensor product of crystals
  • Crystal bases of $U_v^-$
  • The canonical basis
  • Existence and uniqueness (part I)
  • Existence and uniqueness (part II)
  • The Hayashi realization
  • Description of the crystal graph of $V(\Lambda)$
  • An overview of the application to Hecke algebras
  • The Hecke algebra of type $G(m,1,n)$
  • The proof of Theorem 12.5
  • Reference guide
  • Bibliography
  • Index

L'auteur - Susumu Ariki

Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Susumu Ariki
Parution 09/04/2003
Nb. de pages 158
Format 17,5 x 25
Couverture Broché
Poids 295g
Intérieur Noir et Blanc
EAN13 9780821832325
ISBN13 978-0-8218-3232-5

Avantages Eyrolles.com

Livraison à partir de 0,01 en France métropolitaine
Paiement en ligne SÉCURISÉ
Livraison dans le monde
Retour sous 15 jours
+ d'un million et demi de livres disponibles
satisfait ou remboursé
Satisfait ou remboursé
Paiement sécurisé
modes de paiement
Paiement à l'expédition
partout dans le monde
Livraison partout dans le monde
Service clients 0 321 79 56 75 sav@commande.eyrolles.com
librairie française
Librairie française depuis 1925