Geodesic
Various Representations of the Generalized Kostka Polynomials
Séminaire lotharingien de combinatoire, Tome 42 (1998-1999) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

Voir la notice de l'acte

The generalized Kostka polynomials Kl,R(q) are labeled by a partition l and a sequence of rectangles R. They are q-analogues of multiplicities of the finite-dimensional irreducible representation W(l) of gl(n) with highest weight l in the tensor product of the W(R(i))'s. We review several representations of the generalized Kostka polynomials, such as the charge, path space, quasi-particle and bosonic representation. In addition we describe a bijection between Littlewood-Richardson tableaux and rigged configurations, and sketch a proof that it preserves the appropriate statistics. This proves in particular the equality of the quasi-particle and charge representation of the generalized Kostka polynomials. 

@article{SLC_1998-1999_42_a10,
     author = {Anatol N. Kirillov and Anne Schilling and Mark Shimozono},
     title = {Various {Representations} of the {Generalized} {Kostka} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1998-1999},
     volume = {42},
     url = {http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a10/}
}
TY  - JOUR
AU  - Anatol N. Kirillov
AU  - Anne Schilling
AU  - Mark Shimozono
TI  - Various Representations of the Generalized Kostka Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 1998-1999
VL  - 42
UR  - http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a10/
ID  - SLC_1998-1999_42_a10
ER  - 
%0 Journal Article
%A Anatol N. Kirillov
%A Anne Schilling
%A Mark Shimozono
%T Various Representations of the Generalized Kostka Polynomials
%J Séminaire lotharingien de combinatoire
%D 1998-1999
%V 42
%U http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a10/
%F SLC_1998-1999_42_a10
Anatol N. Kirillov; Anne Schilling; Mark Shimozono. Various Representations of the Generalized Kostka Polynomials. Séminaire lotharingien de combinatoire, Tome 42 (1998-1999). http://geodesic.mathdoc.fr/item/SLC_1998-1999_42_a10/