 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1161.11011
Kim, Henry H.
On symmetric powers of cusp forms on GL2. (English)
Weng, Lin (ed.) et al., Papers of the conference on Lfunctions, Fukuoka, Japan, Febru
ary 1823, 2006. Hackensack, NJ: World Scientific. 95113 (2007). ISBN 978981270
5044/hbk
Let = vv be a cuspidal representation of GL2(A), where A is the adele ring of a
number field F. By the local Langlands correspondence, Symm
(v) is an irreducible
admissible representation of GLm+1(Fv) for all v. Consider Symm
() = vSymm
(v).
One of the most important problems in the Langlands program is to show that Symm
()
is automorphic. This is proved up to m = 4 and is due to (H. H. Kim and F. Shahidi
[Ann. Math. (2) 155, No. 3, 837893 (2002; Zbl 1040.11036); J. Am. Math. Soc. 16,
No. 1, 139183 (2003; Zbl 1018.11024)].
The paper under review deals with various properties of symmetric power lifts from
