Classes of unitarizable derived functor modules

Unitarizable weight modules over generalized Weyl algebras

We define a notion of unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring R), which is assumed to carry an involution of the form X∗ = Y , R∗ ⊆ R. We prove that a weight module V is unitarizable iff it is isomorphic to its finitistic dual V . Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necess...

Recollements of Derived Functor Categories ∗ †

We give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [H. Krause, Approximations and adjoints in homotopy categories, Math. Ann. 353 (2012), 765–781]. Then we provide a criterion for the existence of r...

A-infinity algebras, modules and functor categories

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefèvre’s thesis. Finally, starting from an idea of V. Lyubashenko’s, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal catego...

ON THE RESTRICTION OF ZUCKERMAN’S DERIVED FUNCTOR MODULES Aq(λ) TO REDUCTIVE SUBGROUPS

In this article, we study the restriction of Zuckerman’s derived functor (g,K)-modules Aq(λ) to g′ for symmetric pairs of reductive Lie algebras (g, g′). When the restriction decomposes into irreducible (g′,K′)-modules, we give an upper bound for the branching law. In particular, we prove that each (g′,K′)-module occurring in the restriction is isomorphic to a submodule of Aq′ (λ ′) for a parab...

the representations of Sp ( p , q ) and SO ∗ ( 2 n ) unitarily induced from derived functor modules