Classification and partial ordering of reductive Howe dual pairs of classical Lie groups

JOURNAL OF GEOMETRY AND PHYSICS

卷:29

Article

Schmidt, M

关键词: Lie groups;    gauge orbit space;    Howe subgroup;    reductive dual pair;    stratification;   

DOI  :  10.1016/S0393-0440(98)00043-6

来源: Elsevier

【 摘 要 】

Using a general method [C. Moeglin, M.-E Vigneras, J.-L. Waldspurger, Correspondances de Howe sur un Corps p-adique, Lecture Notes in Mathematics, Vol. 1291, Springer, Berlin, 1987] we derive a complete list of conjugacy classes of reductive Howe dual pairs of groups of isometries of real, complex, and quaternionic Hermitian spaces. Moreover, we establish the natural partial ordering on the set of reductive Howe dual pairs which is defined by inclusion module conjugacy. As an application, we determine the singularity structure of the orbit space of a pure SU(n) gauge theory over space-time S-4. (C) 1999 Elsevier Science B.V. All rights reserved. Subj. Class.: Differential geometry 1991 MSG: 22E10; 53C05.

【 授权许可】

Free