Center of infinitesimal Cherednik algebras of 𝔤𝔩_{𝔫}

Tikaradze, Akaki

doi:10.1090/S1088-4165-10-00363-8

Center of infinitesimal Cherednik algebras of $\mathfrak {gl}_n$
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by Akaki Tikaradze

Represent. Theory 14 (2010), 1-8

DOI: https://doi.org/10.1090/S1088-4165-10-00363-8

Published electronically: January 4, 2010

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Abstract:

We show that the center of an infinitesimal Cherednik algebra of $\mathfrak {gl}_n$ is isomorphic to the polynomial algebra of $n$ variables. As consequences of this fact, we show that an analog of Duflo’s theorem holds and all objects in the category $\mathcal {O}$ have finite length.

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