On infinitesimal Cherednik algebras of gl₂
classification
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algebracherednikinfinitesimalcentercharacteristicalgebrasfieldfinitely
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We prove that the center of an infinitesimal Cherednik algebra of $\mf{gl}_2$ is the polynomial algebra of two variables over the field of characteristic 0. In positive characteristic we show that any infinitesimal Cherednik algebra is a finitely generated module over its center.
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