Abstract

In this paper we show that the leading coefficient μ ( y , w ) of certain Kazhdan–Lusztig polynomials P y , w of the permutation group S n of 1 , 2 , … , n are not greater than 1. More precisely, we show that the leading coefficients μ ( y , w ) are not greater than 1 whenever a ( y ) < a ( w ) , where a : S n → N is the function defined in [G. Lusztig, Cells in affine Weyl groups, in: Algebraic Groups and Related Topics, in: Adv. Stud. Pure Math., vol. 6, Kinokunia–North-Holland, 1985, pp. 255–287]. See 1.5 for a simple interpretation of the function a.

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