Report from the National Institute of Allergy and Infectious Diseases workshop on drug allergy

Allergic reactions to drugs are a serious public health concern. In 2013, the Division of Allergy, Immunology, and Transplantation of the National Institute of Allergy and Infectious Diseases sponsored a workshop on drug allergy. International experts in the field of drug allergy with backgrounds in allergy, immunology, infectious diseases, dermatology, clinical pharmacology, and pharmacogenomics discussed the current state of drug allergy research. These experts were joined by representatives from several National Institutes of Health institutes and the US Food and Drug Administration. The participants identified important advances that make new research directions feasible and made suggestions for research priorities and for development of infrastructure to advance our knowledge of the mechanisms, diagnosis, management, and prevention of drug allergy. The workshop summary and recommendations are presented herein.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.