Exponential Decay for Multiple Mixing of Semisimple Actions over Local Fields

In this work, we consider mixing actions of semisimple al-
gebraic groups over local
fields and associated groups. Under certain
conditions on the group and the action, we demonstrate quantitative
decay estimates for the multiple mixing integrals of bounded, K-
finite,
zero-mean functions, focusing on the simplest case where the group is
SL(n;K); n2. These estimates do not depend on Mozes’ theorem on mulitple mixing
and can be used to provide an alternative proof for the groups under
considerations.