Isomorphism of modular group algebras of direct sums of torsion-complete abelian -groups
Biane found out that irreducible decomposition of some representations of the symmetric group admits concentration at specific isotypic components in an appropriate large n scaling limit. This deepened the result on the limit shape of Young diagrams due to Vershik-Kerov and Logan-Shepp in a wider framework. In particular, it is remarkable that asymptotic behavior of the Littlewood-Richardson coefficients in this regime was characterized in terms of an operation in free probability of Voiculescu....
An affine Hecke algebras can be realized as an equivariant -group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by . This...
Les foncteurs entre espaces vectoriels, ou représentations génériques des groupes linéaires d’après Kuhn, interviennent en topologie algébrique et en -théorie comme en théorie des représentations. Nous présentons ici une nouvelle méthode pour aborder les problèmes de finitude et la dimension de Krull dans ce contexte.Plus précisément, nous démontrons que, dans la catégorie des foncteurs entre espaces vectoriels sur , le produit tensoriel entre , où désigne le foncteur projectif , et un foncteur...
Let K be a field of characteristic p > 2 and let G be a group. Necessary and sufficient conditions are obtained so that the group algebra KG is strongly Lie solvable of derived length at most 3. It is also shown that these conditions are equivalent to KG Lie solvable of derived length 3 in characteristic p ≥ 7.