Dg analogues of the Zuckerman functors and the dual Zuckerman functors I

Abstract

We study the category of dg Harish-Chandra modules (over an arbitrary commutative ring) and construct dg analogues of the induction functor, the production functor, the Zuckerman functor and the dual Zuckerman functor.

The proofs of general theorems on symmetric monoidal categories were added. The construction of the differential graded analogue of the dual Zuckerman functor was simplified

References in corpus (7)

• Higher Topos Theory
• On Period Relations for Automorphic L-functions II
• Flat Base Change Formulas for $(\mathfrak{g},K)$-modules over Noetherian rings
• Equivariant analogues of Zuckerman functors
• Symmetries of the hydrogen atom and algebraic families
• Integral models of Harish-Chandra modules of the finite covering groups of PU(1,1)
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors II

Cited by in corpus (7)

• Flat Base Change Formulas for $(\mathfrak{g},K)$-modules over Noetherian rings
• Integral models of Harish-Chandra modules of the finite covering groups of PU(1,1)
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors II
• Families of twisted $\mathcal{D}$-modules and arithmetic models of Harish-Chandra modules
• Uniform decomposition of the flag scheme by a symmetric subgroup action
• $\mathrm{SO}(3)$-homogeneous decomposition of the flag scheme of ${\mathrm{SL}}_3$ over $\mathbb{Z}\left[1/2\right]$
• Filtrations on the globalization of twisted D-modules over Dedekind schemes