If I is the order ideal encircled by the solid line, then [phi](I) is the coset representative
encircled by the solid line, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is labeled by [S.
I] [member of] W is the unique coset representative
of minimum (affine) length.
When we wish to refer to the Poincare polynomial of a minimal length coset representative
w for the induced order on either of the quotients [sup.
In our case, the base window of the minimal length coset representative
of an element is obtained by ordering the entries that appear in the base window increasingly.
1, every coatom w is a maximal-length coset representative
of the subgroup [W.
Any member of the coset determines it and is therefore called a complete set of coset representatives
Furthermore, in order to resolve the scaling problems of Wyler's expression, Gilmore showed why it is essential to use dimensionless volumes by setting the throat sizes of the Anti de Sitter hyperboloids to r = 1, because this is the only choice for r where all elements in the bounded domains are also coset representatives
, and therefore, amount to honest group operations.
The minimal length left coset representatives
[omega] [member of] [[?
A set K formed by a collection of such representatives is called a transversal, and by definition K consists of one and just one point from each distinct coset H + a = [a] (the transversal is also called a complete set of coset representatives
but we shall stick to the shorter name).
J] the set of minimum-length coset representatives
k] denote the set of minimal-length coset representatives
a set of stable and recurrent configurations that form a set of coset representatives
for the critical group.