English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In 1965, Steinberg's study of conjugacy classes in connected reductive groupsled him to construct an affine subspace parametrising regular conjugacyclasses, which he noticed is also a cross section for the conjugation action bythe unipotent radical of a Borel subgroup on another affine subspace. Recently,generalisations of this slice and its cross section property have been obtainedby Sevostyanov in the context of quantum group analogues of W-algebras and byHe-Lusztig in the context of Deligne-Lusztig varieties. Such slices are oftenthought of as group analogues of Slodowy slices.  In this paper we explain their relationship via common generalisationsassociated to Weyl group elements and provide a simple criterion for crosssections in terms of roots. In the most important class of examples thiscriterion is equivalent to a statement about the Deligne-Garside factors oftheir powers in the braid monoid being maximal in some sense. Moreover, we showthat these subvarieties transversely intersect conjugacy classes and determinefor a large class of factorisable r-matrices when the Semenov-Tian-Shanskybracket reduces to a Poisson structure on these slices.

From braids to transverse slices in reductive groups