Conjugacy classes of non-connected semisimple algebraic groups

Consider a non-connected algebraic group G = G ⋉ Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ. The identity component G acts on a fixed exterior component Gτ, id ≠ τ ∈ Γ by conjugation. In this paper we will describe the conjugacy classes and the invariant theory of this action. Let T be a τ -stable maximal torus of G and its Weyl group W. Then the quotient space Gτ//G is isomorphic to (T/(1 − τ )(T))/Wτ. Furthermore, exploiting the Jordan decomposition, the reduced fibres of this quotient map are naturally associated bundles over semisimple G-orbits. Similar to Steinberg's connected and simply connected case [22] and under additional assumptions on the fundamental group of G, a global section to this quotient map exists. The material presented here is a synopsis of the Ph.D thesis of the author, cf. [15

Precision Drift Chambers for the Atlas Muon Spectrometer

ATLAS is a detector under construction to explore the physics at the Large Hadron Collider at CERN. It has a muon spectrometer with an excellent momentum resolution of 3-10%, provided by three layers of precision monitored-drift-tube chambers in a toroidal magnetic field. A single drift tube measures a track point with a mean resolution close to 100 micron, even at the expected high neutron and gamma background rates. The tubes are positioned within the chamber with an accuracy of 20 microns, achieved by elaborate construction and assembly monitoring procedures.Comment: 3 pages, 2 eps figures, Proceedings for poster at Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003. FRAP1

Integral conjugacy classes of compact Lie groups

Abstract.: We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, we review the classification of twisted conjugacy classes of a simply connected compact Lie group G and give a description of their stabilizers in terms of the Dynkin diagram of the corresponding twisted affine Lie algebr

Large-Scale Production of Monitored Drift Tube Chambers for the ATLAS Muon Spectrometer

Precision drift tube chambers with a sense wire positioning accuracy of better than 20 microns are under construction for the ATLAS muon spectrometer. 70% of the 88 large chambers for the outermost layer of the central part of the spectrometer have been assembled. Measurements during chamber construction of the positions of the sense wires and of the sensors for the optical alignment monitoring system demonstrate that the requirements for the mechanical precision of the chambers are fulfilled

Resolution and Efficiency of the ATLAS Muon Drift-Tube Chambers at High Background Rates

The resolution and efficiency of a precision drift-tube chamber for the ATLAS muon spectrometer with final read-out electronics was tested at the Gamma Irradiation Facility at CERN in a 100 GeV muon beam and at photon irradiation rates of up to 990 Hz/square cm which corresponds to twice the highest background rate expected in ATLAS. A silicon strip detector telescope was used as external reference in the beam. The pulse-height measurement of the read-out electronics was used to perform time-slewing corrections which lead to an improvement of the average drift-tube resolution from 104 microns to 82 microns without irradiation and from 128 microns to 108 microns at the maximum expected rate. The measured drift-tube efficiency agrees with the expectation from the dead time of the read-out electronics up to the maximum expected rate

Performance of the ATLAS Precision Muon Chambers under LHC Operating Conditions

For the muon spectrometer of the ATLAS detector at the large hadron collider (LHC), large drift chambers consisting of 6 to 8 layers of pressurized drift tubes are used for precision tracking covering an active area of 5000 m2 in the toroidal field of superconducting air core magnets. The chambers have to provide a spatial resolution of 41 microns with Ar:CO2 (93:7) gas mixture at an absolute pressure of 3 bar and gas gain of 2?104. The environment in which the chambers will be operated is characterized by high neutron and background with counting rates of up to 100 per square cm and second. The resolution and efficiency of a chamber from the serial production for ATLAS has been investigated in a 100 GeV muon beam at photon irradiation rates as expected during LHC operation. A silicon strip detector telescope was used as external reference in the beam. The spatial resolution of a chamber is degraded by 4 ?m at the highest background rate. The detection efficiency of the drift tubes is unchanged under irradiation. A tracking efficiency of 98% at the highest rates has been demonstrated