Twisting operators and centralisers of Lie type groups over local rings

DOI10.1016/J.JALGEBRA.2022.06.029arXiv2006.02145WikidataQ115350271 ScholiaQ115350271MaRDI QIDQ6341988

Publication date: 3 June 2020

Abstract: We extend the classical result asserting that the twisting operator preserves certain Deligne--Lusztig character values for truncated formal power series; along the way we discuss some properties of centralisers. This leads us to the construction of an action of

m a t h r m {G L}_{n} (m a t h b b F_{q} [[p i]] / p i^{r})

on a Springer fibre intersected by Deligne--Lusztig varieties; we determine the primitivities of the induced cohomological representations for single cycles. The case of

m a t h r m {S L}_{2}

over finite dual numbers is presented with a criterion on semisimple orbit representations.

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05)

This page was built for publication: Twisting operators and centralisers of Lie type groups over local rings

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6341988)