Given a root system R and the corresponding finite reflection group W let Hom(W, Z(2) ) be the group of homomorphisms from W into Z(2), where Z(2) ={1, -1} with multiplication. We propose a procedure of constructing subroot systems of R by using homomorphisms eta is an element of Hom(W, Z(2)). This construction is next used for establishing a relation between concepts of total positivity and.-total positivity.
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