Flat Base Change Formulas for $(\mathfrak{g},K)$-modules over Noetherian rings

Abstract

The fucntor $I$ and its derived functor over the complex number field have been playing important roles in representation theory of real reductive Lie groups. In this paper, we discuss the flat base change formulas of the functor I and its derived functor over Noetherian rings. In particular, a flat base change theorem for $A_{\mathfrak{q}}(\lambda )$ is obtained.

arXiv comment34 pages

References in corpus (8)

• Higher Topos Theory
• Semisimple corings
• A general framework for homotopic descent and codescent
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors I
• On Period Relations for Automorphic L-functions II
• Integral models of Harish-Chandra modules of the finite covering groups of PU(1,1)
• A Second Adjoint Theorem for SL(2,R)
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors II

Cited by in corpus (7)

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• Integral models of Harish-Chandra modules of the finite covering groups of PU(1,1)
• Families of twisted $\mathcal{D}$-modules and arithmetic models of Harish-Chandra modules
• $\mathrm{SO}(3)$-homogeneous decomposition of the flag scheme of ${\mathrm{SL}}_3$ over $\mathbb{Z}\left[1/2\right]$
• Rationality patterns
• Filtrations on the globalization of twisted D-modules over Dedekind schemes