Finite Analytic Characters and Tannakian Source Reconstruction: A Finite Tensor–Quiver Framework for Beyond Endoscopy
This paper organizes finite tensor–quiver reconstruction for reductive source data. For a fixed reductive Zariski-closed subgroup H of a reductive complex group G and a faithful finite-dimensional representation, the standard mixed-tensor reconstruction theorem and Noetherianity imply that finitely many H-invariant tensors have common stabilizer H. Classical quiver invariant theory then implies that finitely many traces of oriented cycles separate closed orbits, including semisimple realizations. For GL₂/ℚ, we give a restricted application of Cheng’s symmetric-square limiting distribution.…
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