Extended packet conjecture

Suppose bbGbbG is bbFbbF-quasi-split and fix a Whittaker datum (bbU,bbpsi)(bbU,bbpsi). An extended LL-packet is a fibre of the composite semisimplification map from representations to semisimple parameters. Extended packet conjecture. Every extended LL-packet contains a unique bbpsibbpsi-generic representation.

The source notes that this would follow, under the stated local Langlands conjecture, from the tempered packet conjecture and the maximal-monodromy formulation of Gross–Prasad–Rallis. The supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Jean-François Dat, David Helm, Robert Kurinczuk and Gilbert Moss, “Local Langlands in families: The banal case”, arXiv:2406.09283 (2024).

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