Original paper

Commentarii Mathematici Helvetici

, Volume 78, Issue 4, pp 663-680

First online:

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

  • Tôru UmedaAffiliated withDepartment of Mathematics, Faculty of Science, Kyoto University

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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