TY - JOUR
T1 - On the images of Galois representations attached to low weight Siegel modular forms
AU - Weiss, Ariel
N1 - Publisher Copyright:
© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - Let (Formula presented.) be a cuspidal automorphic representation of (Formula presented.), whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If (Formula presented.) is not CAP or endoscopic, then we show that its associated (Formula presented.) -adic Galois representations are irreducible and crystalline for (Formula presented.) of primes (Formula presented.). If, moreover, (Formula presented.) is neither an automorphic induction nor a symmetric cube lift, then we show that, for (Formula presented.) of primes (Formula presented.), the image of its mod (Formula presented.) Galois representation contains (Formula presented.).
AB - Let (Formula presented.) be a cuspidal automorphic representation of (Formula presented.), whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If (Formula presented.) is not CAP or endoscopic, then we show that its associated (Formula presented.) -adic Galois representations are irreducible and crystalline for (Formula presented.) of primes (Formula presented.). If, moreover, (Formula presented.) is neither an automorphic induction nor a symmetric cube lift, then we show that, for (Formula presented.) of primes (Formula presented.), the image of its mod (Formula presented.) Galois representation contains (Formula presented.).
UR - http://www.scopus.com/inward/record.url?scp=85127775717&partnerID=8YFLogxK
U2 - 10.1112/jlms.12576
DO - 10.1112/jlms.12576
M3 - Article
AN - SCOPUS:85127775717
SN - 0024-6107
VL - 106
SP - 358
EP - 387
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 1
ER -