Springer's work on unipotent classes and Weyl group representations

2020/07/21 by G. Lusztig, Lusztig, G.
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2007.11996

openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety, Springer's example of nonrationality of certain representations of the Hecke algebras associated to a Weyl group and the Springer representation of the Weyl group associated to a unipotent element.

Related

• Remarks on Springer's representations
• From families in Weyl groups to Springer representations
• Families and Springer's correspondence
• Unipotent classes and special Weyl group representations
• A new basis for the representation ring of a Weyl group, II