The decomposition into left cells of the affine Weyl group of type \(\widetilde D_ 4\)
\textit{D. Kazhdan} and \textit{G. Lusztig} [Invent. Math. 53, 165-184 (1979; Zbl 0499.20035)] defined the concepts of left, right, and two-sided cells for a Coxeter group which play an important role in the representation theory of its associated Hecke algebra. In this paper the author describes all 508 left cells in the affine Weyl group \(W\) of type \(\widetilde{D}_ 4\) by using the canonical expression of the elements of \(W\), and the author also finds all 508 distinguished involutions for \(W\).
affine Weyl group of type \(\widetilde{D}_ 4\)
scientific article; zbMATH DE number 554143