English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the endomorphism algebras attached to Bernstein components ofreductive $p$-adic groups and construct a local Langlands correspondence withthe appropriate set of enhanced $L$-parameters, using certain "desiderata"properties for the LLC for supercuspidal representations of proper Levisubgroups. We give several applications of our LLC to various reductive groupswith Bernstein blocks cuspidally supported on general linear groups.  In particular, for Levi subgroups of maximal parabolic of the splitexceptional group $G_2$, we compute the explicit weight functions for thecorresponding Hecke algebras, and show that they satisfy a conjecture ofLusztig's. Some results from $\S 4$ are used by the same authors to construct afull local Langlands correspondence in \cite{AX-LLC}. Moreover, we also prove areduction to depth zero case result for the Bernstein components attached toregular supercuspidal representations of Levi subgroups.

Hecke algebras for $p$-adic reductive groups and Local Langlands Correspondence for Bernstein blocks