In this paper we prove Vogan's conjecture on Arthur packets for general linear groups over p-adic fields, building on earlier work. The proof uses a special case of endoscopic lifting, adapted from the 1992 book by Adams, Barbasch and Vogan, where it was articulated for real groups.
Data assimilation refers to a set of techniques used to combine observational information with numerical models for chaotic dynamical systems and provides a rich interface between dynamical and statistical methodologies in nonlinear dynamics. The main aim of this paper is to compare and contrast two extensively studied paradigms in each of these approaches: on one hand, the ensemble Kalman filter which is a statistical estimation technique, and on the other hand, chaotic synchronization that has been studied in many other contexts, by viewing synchronization as a data assimilation method. In particular, we study the sensitivity of these two methods to changes in observational noise and observational frequency, using both simulated observations and data obtained from an experimental realization of a commonly used low-dimensional dynamical system, namely, Chua circuit, in both the periodic as well as the chaotic regime.
In this paper we prove Vogan’s conjecture on local Arthur packets, as recalled in Cunningham et al. [Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples, Memoirs of the American Mathematical Society, Boston, 2022, Section 8.3, Conjecture 1(a)], for irreducible Arthur parameters of p-adic general linear groups. This result shows that these Arthur packets may be characterized by properties of simple perverse sheaves on a moduli space of Langlands parameters.
In this paper we prove Vogan's conjecture on local Arthur packets, as recalled in [CFM + 22, Section 8.3, Conjecture 1(a)], for Arthur parameters of p-adic general linear groups that are irreducible and trivial on the Weil group -we refer to such parameters as simple Arthur parameters. This result shows that these Arthur packets may be characterized by properties of simple perverse sheaves on a moduli space of Langlands parameters.
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