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On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$

A. A. Tarasov

M. V. Lomonosov Moscow State University

Abstract: For the Lie algebra $\mathfrak g=\mathfrak{gl}(n,\mathbb C)$ it is proved that the maximal commutative subalgebras of the Poisson algebra $P(\mathfrak g)$ obtained by the method of shifting the invariants can be lifted to the enveloping algebra. Moreover, this lifting can be carried out by means of the symmetrization map.

UDC: 519.46

MSC: Primary 17B35; Secondary 16S30, 17B45, 17B63

Received: 13.10.1999

DOI: 10.4213/sm509

 English version: Sbornik: Mathematics, 2000, 191:9, 1375–1382

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