Some remarks on a result of Jensen and tilting modules for $\SL_3(k)$ and $q$-$\GL_3(k)$

Abstract

This paper reviews a result of Jensen on characters of some tilting modules for $\SL_3(k)$, where $k$ has characteristic at least five and fills in some gaps in the proof of this result. We then apply the result to finding some decomposition numbers for three part partitions for the symmetric group and the Hecke algebra. We review what is known for characteristic two and three. The quantum case is also considered: analogous results hold for the mixed quantum group where $q$ is an $l$th root of unity with $l$ at least three and thus also hold for the associated Hecke algebra.

arXiv comment18 pages, 8 figures

Cited by in corpus (2)

• Billiards and Tilting Characters for ${\mathrm{SL}}_3$
• Decomposition of Tensor Products of Modular Irreducible Representations for $S{L}_3$: the $p\ge 5$ case