Geodesic
Graded limits of minimal affinizations and beyond: the multiplicity free case for type~$E_6$
Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 69-115

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type $E_6$. For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the associated quantum group. We prove that this is the case under further restrictions on the highest weight. Under another set of conditions on the highest weight, Chari and Greenstein have recently proved that they are projective objects of a full subcategory of the category of graded modules for the current algebra. Our formula applies to all of these projective modules.
Keywords: minimal affinizations of quantum groups, character formulae, affine Kac-Moody algebras. 
@article{ADM_2011_12_1_a4,
     author = {Adriano Moura and Fernanda Pereira},
     title = {Graded limits of minimal affinizations and beyond: the multiplicity free case for type~$E_6$},
     journal = {Algebra and discrete mathematics},
     pages = {69--115},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a4/}
}
TY  - JOUR
AU  - Adriano Moura
AU  - Fernanda Pereira
TI  - Graded limits of minimal affinizations and beyond: the multiplicity free case for type~$E_6$
JO  - Algebra and discrete mathematics
PY  - 2011
SP  - 69
EP  - 115
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a4/
LA  - en
ID  - ADM_2011_12_1_a4
ER  - 
%0 Journal Article
%A Adriano Moura
%A Fernanda Pereira
%T Graded limits of minimal affinizations and beyond: the multiplicity free case for type~$E_6$
%J Algebra and discrete mathematics
%D 2011
%P 69-115
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a4/
%G en
%F ADM_2011_12_1_a4
Adriano Moura; Fernanda Pereira. Graded limits of minimal affinizations and beyond: the multiplicity free case for type~$E_6$. Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 69-115. http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a4/