\(P\)-kernels, IC bases and Kazhdan-Lusztig polynomials
The author shows that, under some mild hypotheses, the concept of a \(P\)-kernel for any locally finite partially ordered set \(P\) and the concept of an IC basis are equivalent, where the concept of a \(P\)-kernel for any locally finite partially ordered set \(P\) was introduced by \textit{R. P. Stanley} [in J. Am. Math. Soc. 5, No. 4, 805-851 (1992; Zbl 0768.05100)] and the concept of an IC basis was introduced by \textit{J. Du} [in Proc. Symp. Pure Math. 56, Pt. 2, 135-148 (1994; Zbl 0813.17010)]. For a given Coxeter group \(W\), partially ordered by the Bruhat order, the author shows that the \(W\)-kernel corresponds to the Kazhdan-Lusztig basis of the Hecke algebra of \(W\). The author shows that this \(W\)-kernel factorizes as a product of other \(W\)-kernels, and that these provide a solution to the Yang-Baxter equations for \(W\).
scientific article; zbMATH DE number 1891337
scientific article