This splits off the first issue of #15475 (which has already been reviewed by Darij). This will also address the issues noted on https://groups.google.com/forum/#!topic/sage-devel/rXobHQXrCck.

CC: @darijgr

Component: coercion

Keywords: symmetric group algebra, descent algebra

Author: Travis Scrimshaw

Branch: d8ea764

Reviewer: Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/16678