Algebraic approach to contraction families

Abstract

In this paper, we give a purely algebraic approach to the contraction group scheme predicted by Bernstein--Higson--Subag and constructed by Barbasch--Higson--Subag. We also compare quotient schemes of contraction group schemes with other related schemes, equipped with actions of contraction group schemes in the cases of symmetric and $\hat{I}¸$-stable parabolic subgroups.

The statement of Lemma 4.1 was given over general base schemes. The arguments in Section 4.1 were extended. Example 2.12 was added for new contents of Section 4.1