English

Center of Kostant algebra

Representation Theory 2025-09-25 v1

Abstract

In this note, following Mui\'c-Savin, we compute the center of Kostant algebra, introduced by Kostant in 1975 as strongly commuting algebra. We explain how it encodes information on tensor products between a finite-dimensional and a Verma module, and about the structure of principal series representations via the work of Bernstein-Gelfand. We also discuss conjectured relationships to Langlands duality.

Keywords

Cite

@article{arxiv.2509.20159,
  title  = {Center of Kostant algebra},
  author = {Tamás Hausel},
  journal= {arXiv preprint arXiv:2509.20159},
  year   = {2025}
}

Comments

21 pages, 5 figures, to appear in "G\'eom\'etrie Alg\'ebrique et Programme de Langlands un volume en l'honneur de G\'erard Laumon"