literature
Literature
Authors
Jobs
Seminars
Conferences
DataBETA

Symmetrisation and the Feigin–Frenkel centre

May 19, 2022
38 pages
Published in:
  • Compos.Math. 158 (2022) 3, 585-622
  • Published: May 19, 2022
DOI:
View in:
reference search2 citations

Citations per year

20212022202302
Abstract: (Cambridge University Press)
For complex simple Lie algebras of types B, C, and D, we provide new explicit formulas for the generators of the commutative subalgebra z(g^)⊂U(t−1g[t−1])\mathfrak z(\hat {\mathfrak g})\subset {{\mathcal {U}}}(t^{-1}\mathfrak g[t^{-1}]) known as the Feigin–Frenkel centre. These formulas make use of the symmetrisation map as well as of some well-chosen symmetric invariants of g\mathfrak g. There are some general results on the rôle of the symmetrisation map in the explicit description of the Feigin–Frenkel centre. Our method reduces questions about elements of z(g^)\mathfrak z(\hat {\mathfrak g}) to questions on the structure of the symmetric invariants in a type-free way. As an illustration, we deal with type G2_2 by hand. One of our technical tools is the map m ⁣ ⁣:Sk(g)→Λ2g⊗Sk−3(g){\sf m}\!\!: {{\mathcal {S}}}^{k}(\mathfrak g)\to \Lambda ^{2}\mathfrak g \otimes {{\mathcal {S}}}^{k-3}(\mathfrak g) introduced here. As the results show, a better understanding of this map will lead to a better understanding of z(g^)\mathfrak z(\hat {\mathfrak g}).
  • Kac–Moody algebra
  • symmetric invariants
  • Segal–Sugawara vectors
  • 16S30
  • 17B67
  • 17B20
  • 17B35
  • 17B63
  • 1-25 of 33
  • 1
  • 2
  • 25 / page