Equivalence of categories between coefficient systems and systems of idempotents

Abstract

The consistent systems of idempotents of Meyer and Solleveld allow to construct Serre subcategories of Rep R ⁡ ( G ) \operatorname {Rep}_R(G) , the category of smooth representations of a p p -adic group G G with coefficients in R R . In particular, they were used to construct level 0 decompositions when R = Z ¯ ℓ R=\overline {\mathbb {Z}}_{\ell } , ℓ ≠ p \ell \neq p , by Dat for G L n GL_{n} and the author for a more general group. Wang proved in the case of G L n GL_{n} that the subcategory associated with a system of idempotents is equivalent to a category of coefficient systems on the Bruhat-Tits building. This result was used by Dat to prove an equivalence between an arbitrary level zero block of G L n GL_{n} and a unipotent block of another group. In this paper, we generalize Wang’s equivalence of category to a connected reductive group on a non-archimedean local field.

Different Numerical Techniques, Modeling and Simulation in Solving Complex Problems

“…Furthermore, [19] also highlights the importance of uncertainty quantification in modeling and simulation. Uncertainty quantification is the process of quantifying the uncertainty in the model's predictions, and can be used to identify sources of uncertainty, to propagate uncertainty through the model, and to assess the model's robustness and reliability.…”