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 ${\mathbb{Z}}_{\ell }$-spets (as defined in our earlier paper), motivated by analogous statements for finite groups. We show that these conjectures hold in certain situations. For this we introduce and study a Yokonuma type algebra for torus normalisers in $\ell$-compact groups which may be of independent interest.

slightly revised and reorganised version

References in corpus (1)

• The freeness and trace conjectures for parabolic Hecke subalgebras