Abstract
Let (W,S) be a Weyl group of type Bn. In this paper, we find certain nontrivial distinguished involutions in the two-sided cell Ωt of W with a-value [Formula: see text] for 1≤ 2t ≤ n and n even (resp., [Formula: see text] for 1≤ 2t < n and n odd). Besides, for 1≤ i1< ⋯ < it≤ n-1, let Li1⋯ it be a left cell of W with a-value t2 and R(Li1⋯ it) ={si1,…,sit}. There are only two involutions y(i1,i1)⋯ y(it-1,it-1) sit and y(i1,i1)⋯ y(it,it) in the left cell Li1⋯ it. We prove that the former (resp., latter) is a distinguished involution in the left cell Li1⋯ it for t odd (resp., even).
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