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

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.Comment: 34 page

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

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.Comment: 38 page

Asymptotics for penalized spline estimators in quantile regression

Quantile regression predicts the $\tau$-quantile of the conditional distribution of a response variable given the explanatory variable for $\tau\in(0,1)$. The aim of this paper is to establish the asymptotic distribution of the quantile estimator obtained by penalized spline method. A simulation and an exploration of real data are performed to validate our results.Comment: 20 pages, 11 figure