The generalized lifting property of Bruhat intervals

In Tsukerman and Williams (Adv Math 285: 766–810, 2015), it is shown that every Bruhat interval of the symmetric group satisfies the so-called generalized lifting property. In this paper, we show that a Coxeter group satisfies this property if and only if it is finite and simply-laced.     

Special idempotents and projections

Semigroup Forum - We define, for any special matching of a finite graded poset, an idempotent, regressive and order preserving function. We consider the monoid generated by such functions. We call...