Commentarii Mathematici Helvetici

, Volume 78, Issue 4, pp 663–680

Application of Koszul complex to Wronski relations for $U(\frak{gl}_n)$

  • Tôru Umeda
Original paper

DOI: 10.1007/s00014-003-0784-7

Cite this article as:
Umeda, T. Comment. Math. Helv. (2003) 78: 663. doi:10.1007/s00014-003-0784-7


Explicit relations between two families of central elements in the universal enveloping algebra $U(\frak{gl}_n)$ of the general linear Lie algebra $\frak{gl}_n$ are presented. The two families of central elements in question are the ones expressed respectively by the determinants and the permanents: the former are known as the Capelli elements, and the latter are the central elements obtained by Nazarov. The proofs given are based on the exactness of the Koszul complex and the Euler-Poincaré principle.

Mathematics Subject Classification (2000)

17B35 15A15 16Exx 


Center of universal enveloping algebra Capelli elements Koszul complex Wronski relations 

Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  • Tôru Umeda
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan

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