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 prove Lusztig's conjectures ${\bf P1}$-${\bf P15}$ for the affine Weylgroup of type $\tilde{C}_2$ for all choices of positive weight function. Ourapproach to computing Lusztig's $\mathbf{a}$-function is based on the notion ofa `balanced system of cell representations'. Once this system is establishedroughly half of the conjectures ${\bf P1}$-${\bf P15}$ follow. Next weestablish an `asymptotic Plancherel Theorem' for type $\tilde{C}_2$, from whichthe remaining conjectures follow. Combined with existing results in theliterature this completes the proof of Lusztig's conjectures for all rank $1$and $2$ affine Weyl groups for all choices of parameters.

Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for $\tilde{C}_2$