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Title: On the reflection type decomposition of the adjoint reduced phase space of a compact semisimple Lie group

We consider a system with symmetries whose configuration space is a compact Lie group, acted upon by inner automorphisms. The classical reduced phase space of this system decomposes into connected components of orbit type subsets. To investigate hypothetical quantum effects of this decomposition one has to construct the associated costratification of the Hilbert space of the quantum system in the sense of Huebschmann. In the present paper, instead of the decomposition by orbit types, we consider the related decomposition by reflection types (conjugacy classes of reflection subgroups). These two decompositions turn out to coincide, e.g., for the classical groups SU(n) and Sp(n). We derive defining relations for reflection type subsets in terms of irreducible characters and discuss how to obtain from that the corresponding costratification of the Hilbert space of the system. To illustrate the method, we give explicit results for some low rank classical groups.
Authors:
 [1] ; ;  [2]
  1. Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, 57068 Siegen (Germany)
  2. Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig (Germany)
Publication Date:
OSTI Identifier:
22224161
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 8; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONFIGURATION; HILBERT SPACE; ORBITS; PHASE SPACE; SET THEORY; SU GROUPS