The principal block of a Zℓ-spets and Yokonuma type algebras

Radha Kessar; Gunter Malle; Jason Semeraro

doi:10.2140/ant.2023.17.397

The principal block of a Z_ℓ-spets and Yokonuma type algebras

Radha Kessar, Gunter Malle, Jason Semeraro

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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 certain situations. For this we introduce and study a Yokonuma type algebra for torus normalisers in ℓ-compact groups which may be of independent interest.

Original language	English
Pages (from-to)	397-433
Number of pages	37
Journal	Algebra and Number Theory
Volume	17
Issue number	2
DOIs	https://doi.org/10.2140/ant.2023.17.397
Publication status	Published - 24 Mar 2023

Keywords

principal block
spetses
Yokonuma type algebra
ℓ-adic reflection groups

Access to Document

10.2140/ant.2023.17.397Licence: CC BY

Cite this

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abstract = "We formulate conjectures concerning the dimension of the principal block of a Zℓ-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 ℓ-compact groups which may be of independent interest.",

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KW - spetses

KW - Yokonuma type algebra

KW - ℓ-adic reflection groups

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