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Macdonald formula for spherical functions on affine buildings

A. M. Mantero, A. Zappa (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

Modular representations of finite groups with trivial restriction to Sylow subgroups

Paul Balmer (2013)

Journal of the European Mathematical Society

Let k be a field of characteristic p . Let G be a finite group of order divisible by p and P a p -Sylow subgroup of G . We describe the kernel of the restriction homomorphism T ( G ) T ( P ) , for T ( ) the group of endotrivial representations. Our description involves functions G k × that we call weak P -homomorphisms. These are generalizations to possibly non-normal P G of the classical homomorphisms G / P k × appearing in the normal case.

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