The principal block of a $\mathbb{Z}_\ell$-spets and Yokonuma type algebras

Abstract

We formulate conjectures concerning the dimension of the principal block of a Z ℓ -spets (as defined in our earlier paper), motivated by analogous statements for finite groups. We show that these conjectures hold in a large number of cases. For this we introduce and study a Yokonuma type algebra for torus normalisers in ℓ-compact groups which may be of independent interest.