Wavefront sets for genuine irreps of Kazhdan-Patterson and Savin GL-covers are determined from the degrees of their highest Bernstein-Zelevinsky derivatives, with a Langlands reinterpretation for the former.
On the upper bound of wavefront sets of representations of p-adic groups
1 Pith paper cite this work. Polarity classification is still indexing.
abstract
In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper bound and show that it can be reduced to that of anti-discrete series representations, namely, those whose Aubert-Zelevinsky duals are discrete series. Then, we show that this conjecture is equivalent to the Jiang conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogous conjecture on the upper bound of wavefront sets of representations in local ABV packets.
fields
math.RT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Wavefront sets for genuine representations of $\rm GL$-covers of Kazhdan--Patterson or Savin types
Wavefront sets for genuine irreps of Kazhdan-Patterson and Savin GL-covers are determined from the degrees of their highest Bernstein-Zelevinsky derivatives, with a Langlands reinterpretation for the former.