Recall that a kernel conditionaly of negative type on a set X is a map psi:XtimesXrightarrowmathbbR with the following properties:
1) psi(x,x)=0
2) psi(y,x)=psi(x,y)
3) for any elements x1,...xn and all real numbers c1,...,cn, with c1+...+cn=0, the following inequality holds:
sumni=1sumnj=1cicjpsi(xi,xj)leq0.
Let G be a discrete group.
Recall that a function GrightarrowmathbbR is conditionally of
negative type if the kernel psi, defined by psi(g,h)=psi(h−1g) is conditionaly of negative type.
Does there exist class of discrete groups which admit an explicit description of functions which are conditionaly of negative type?
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