Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Kim, Henry H.
On symmetric powers of cusp forms on GL2. (English)
Weng, Lin (ed.) et al., Papers of the conference on L-functions, Fukuoka, Japan, Febru-
ary 1823, 2006. Hackensack, NJ: World Scientific. 95-113 (2007). ISBN 978-981-270-
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
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