Triality and Functoriality

Gaëtan Chenevier; Wee Teck Gan

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arXiv · 2510.21169

Triality and Functoriality

Gaëtan Chenevier·Wee Teck Gan

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Abstract

We use the triality automorphism of simple algebraic groups of type $D_4$ to prove some new instances of global Langlands functorial lifting. In particular, we prove the (weak) spin lifting from ${\rm GSp}_6$ to ${\rm GL}_8$ and the tensor product lifting from ${\rm GL}_2 \times {\rm GSp}_4$ to ${\rm GL}_8$. As an arithmetic application, we establish the expected properties of the spinor L-function attached to an arbitrary Siegel modular cusp form for ${\rm Sp}_6(\mathbb{Z})$ generating a holomorphic discrete series.

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Gaëtan Chenevier, Wee Teck Gan. 2025-10-24. Triality and Functoriality. https://arxiv.org/abs/2510.21169

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