Show that, for A ∈Ξ(n, ⩽r)^ ±, ξA^- ; 0 ξA^+ ; 0=ξA^' 0+f, ξA^+ ; 0 ξA^- ; 0=ξA ; 0+g in 𝒮(n,

Question

Show that, for A ∈Ξ(n, ⩽r)^ ±, ξA^- ; 0 ξA^+ ; 0=ξA^' 0+f,   ξA^+ ; 0 ξA^- ; 0=ξA ; 0+g in 𝒮(n,

Accepted Answer

Step 1: Understand the notation and definitions.u000Au002D $u005CXi(n, u005Cleqslant r)^{u005Cpm}$ refers to a set o

Show that, for $A \in \Xi(n, \leqslant r)^{ \pm}$, $$ \xi_{A^{-} ; 0} \xi_{A^{+} ; 0}=\xi_{A^{\prime} 0}+f, \quad \xi_{A^{+} ; 0} \xi_{A^{-} ; 0}=\xi_{A ; 0}+g $$ in $\mathcal{S}(n, r)$, where $f, g$ are $\mathbb{Q}(v)$-linear combination of $\xi_{B ; j}$ with $B \prec A$, $j \in \mathbb{Z}^n$.