engleski

Zuckerman functors between equivariant derived categories

We review the Beilinson-Ginzburg construction of equivariant derived categories of Harish-Chandra modules, and introduce analogues of Zuckerman functors in this setting. They are given by an explicit formula, which works equally well in the case of modules with a given infinitesimal character. This is important if one wants to apply Beilinson-Bernstein localization, as is explained in [MP1]. We also show how to recover the usual Zuckerman functors from the equivariant ones by passing to cohomology.

Harish-Chandra modules; Zuckerman functors; equivariant derived categories

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