W-graph ideals and biideals

We further develop the theory of $W\!$-graph ideals, first introduced by the authors in reference [6]. We discuss $W\!$-graph subideals, and induction and restriction of $W\!$-graph ideals for parabolic subgroups. We introduce $W\!$-graph biideals: those $W\!$-graph ideals that yield $(W\times W^{\mathrm o})$-graphs, where $W^{\mathrm o}$ is the group opposite to $W$. We determine all $W\!$-graph ideals and biideals in finite Coxeter groups of rank 2.

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