Abstract
W -graphs are closely connected with Kazhdan-Lustig polynomials, arising in connection with problems of the theory of representations of semisimple groups. For the symmetric group Sh a description is known of the Kazhdan-Lustig polynomials and the W -graphs connected with them for the Grassman manifolds. The goal of this paper is a combinatorial description of more general graphs. In particular, the graphs of hooks and all irreducible W -graphs for n=6 are found.
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