Secondary Quantum Hamiltonian Reduction

Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general $sl(2)$ embeddings into Lie (super)algebras, and in the case of general $osp(1|2)$ embeddings into Lie superalgebras. In another development it has been shown that when $H$ and $H'$ are both subalgebras of a Lie algebra $G$ with $H'\subset H$, then classically the $W(G,H)$ algebra can be obtained by performing a secondary hamiltonian reduction on $W(G,H')$. In this paper we show that the corresponding statement is true also for quantum hamiltonian reduction when the simple roots of $H'$ can be chosen as a subset of the simple roots of $H$. As an application, we show that the quantum secondary reductions provide a natural framework to study and explain the linearization of the $W$ algebras, as well as a great number of new realizations of $W$ algebras.Comment: 33 pages, LATEX. Final version, including proof of conjecture. Accepted for publication in Comm. Math. Phy

Extended Superconformal Algebras from Classical and Quantum Hamiltonian Reduction

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These have recently been neatly classified by several groups, and we emphasize the classification based on hamiltonian reduction of affine Lie superalgebras with even subalgebras $G\oplus sl(2)$. We reveiw the situation and improve on previous formulations by presenting generic and very compact expressions valid for all algebras, classical and quantum. Similarly generic and compact free field realizations are presented as are corresponding screening charges. Based on these a discussion of singular vectors is presented. (Based on talk by J.L. Petersen at the Int. Workshop on "String Theory, Quantum Gravity and the Unification of the Fundamental Interactions", Rome Sep. 21-26, 1992)Comment: 30 pages, NBI-HE-92-8

Immunohistochemical staining for S-lOO and GFAP proteins of spontaneous brain tumours in Wistar rats

The occurrence of spontaneous brain tumours in rats is relatively rare. The need for a histological correct classification of rat brain tumours is of great importance in evaluation of chemical induced brain neoplasms in long term carcinogenicity studies.The value of additional immunohistochemical staining for GFAP and S-100 proteins were investigated in a long term carcinogenicity study. Astrocytomas were positive for the GFAP protein but no tumours had a clear positive reaction for the S-100 protein. The most common tumour type was granular cell tumour which did not stain for the GFAP and S-100 proteins. However one tumour of this type had a subpopulation of cells that stained for GFAP protein. In the light of the relatively few astrocytomas in the material, no firm conclusion on the value of staining for GFAP protein can be drawn. However the investigation suggests that staining for GFAP protein is of value in the diagnosis ofastrocytomas. Staining for S-100 protein did not show a positive reaction in any ofthe tumours. In conclusion staining for S-100 protein in this study did not have any diagnostic value

The Strange Star Surface: A Crust with Nuggets

We reexamine the surface composition of strange stars. Strange quark stars are hypothetical compact stars which could exist if strange quark matter was absolutely stable. It is widely accepted that they are characterized by an enormous density gradient ($~10^{26}$ g/cm$^4$) and large electric fields at surface. By investigating the possibility of realizing a heterogeneous crust, comprised of nuggets of strange quark matter embedded in an uniform electron background, we find that the strange star surface has a much reduced density gradient and negligible electric field. We comment on how our findings will impact various proposed observable signatures for strange stars.Comment: 4 pages, 2 figure