 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1124.22004
Hsie, Bingyong
Mackey theory for padic Lie groups. (English)
Acta Math. Sin., Engl. Ser. 22, No. 2, 507514 (2006). ISSN 14398516; ISSN 1439
7617
http://dx.doi.org/10.1007/s1011400505362
http://www.springerlink.com/content/104538/
Let H be a finite group acting on a finite abelian group A. Let G denote the semidirect
product of H by A. The method of little groups of Wigner and Mackey classifies all
the irreducible representations of G as certain induced representations. The method
also works in the situation of Hilbert space representations of separable locally compact
groups and this is due to G. W. Mackey [Ann. Math. (2) 58, 193221 (1953; Zbl
0051.01901)]. In the special case of the PoincarŽe group, Mackey's result goes back to
E. P. Wigner [Ann. Math. (2) 40, 149204 (1939; Zbl 0020.29601)]. Closely following
Mackey, the paper under review gives a padic analogue of WignerMackey theory. The
precise result is as follows: Let A be a locally compact totally disconnected abelian
group such that its dual A has the same property. Let H be a locally compact totally
disconnected group with a continuous action t on A, and a dual action t on A. Let
