Symmetric power functoriality for holomorphic modular forms
Symmetric power functoriality for holomorphic modular forms
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Jack Thorne, University of Cambridge
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Langlands鈥檚 functoriality conjectures predict the existence of 鈥渓iftings鈥 of automorphic representations along morphisms of L-groups. A basic case of interest comes from the irreducible algebraic representations of GL(2), thought of as the L-group of the reductive group GL(2) over Q. I will discuss the proof, joint with James Newton, 听of the existence of the corresponding functorial liftings for a broad class of holomorphic modular forms, including Ramanujan鈥檚 Delta function.