Lie algebras
Dans cet article, on classifie les modules de plus haut poids unitarisables sur la super-algèbre de Virasoro tordue.
We construct a family of non-weight modules which are free -modules of rank 2 over the super Schrödinger algebra in -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free -modules of rank 2 over are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
Let be a complex reductive Lie algebra and be any reductive in subalgebra. We call a -module bounded if the -multiplicities of are uniformly bounded. In this paper we initiate a general study of simple bounded -modules. We prove a strong necessary condition for a subalgebra to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded -module, and then establish a sufficient condition for a subalgebra to be bounded (Theorem 5.1). As a result we are able to...
We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures...