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

TL;DR

This paper establishes flat base change formulas for the functor I and its derived functor in the context of $(\mathfrak{g},K)$-modules over Noetherian rings, extending classical results over complex numbers.

Contribution

It introduces flat base change formulas for $(\mathfrak{g},K)$-modules over Noetherian rings, including a new theorem for $A_{\mathfrak{q}}(\lambda)$.

Findings

Derived flat base change theorem for $A_{\mathfrak{q}}(\lambda)$

Extension of base change formulas to Noetherian ring setting

Enhanced understanding of functor behavior over more general 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.