Triality and Functoriality

2025/10/24 by Chenevier, Gaëtan, Gan, Wee Teck · 1 citation
#11F27 #11F46 #11F55 #11F66 #11F70 #11F80 #11R39 #20E50 #20E55 #20G41 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.21169

Abstract

We use the triality automorphism of simple algebraic groups of type D₄ to prove some new instances of global Langlands functorial lifting. In particular, we prove the (weak) spin lifting from \rm GSp₆ to \rm GL₈ and the tensor product lifting from \rm GL₂ × \rm GSp₄ to \rm GL₈. As an arithmetic application, we establish the expected properties of the spinor L-function attached to an arbitrary Siegel modular cusp form for \rm Sp₆(ℤ) generating a holomorphic discrete series.

Citations

• Local Intertwining Relations and Co-tempered A-packets of Classical Groups
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• Generic Transfer for General Spin Groups
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Cited by

• Triality and adjoint lifting for GL(3)

Related

• Towards Functoriality Of Spinor L-functions
• Level-raising and symmetric power functoriality, I
• Level-raising and symmetric power functoriality, III
• Triality and adjoint lifting for GL(3)
• Triality in so(4,4), characteristic classes, D4 and G2 singularities