“…Sections [5][6][7][8] show that nearly all examples of fine S n -characters mentioned earlier have natural B n -analogues. These include the irreducible characters of B n , the Gelfand model, the characters of the natural B n -action on the homogeneous components of the coinvariant algebra of type B, signed analogues of the Lie characters, characters induced from exterior algebras and k-root enumerators, with corresponding fine sets consisting of elements of Knuth classes of type B n , involutions, signed permutations of fixed flaginversion number or flag-major index, conjugacy classes in B n , signed analogues of arc permutations and k-roots of the identity signed permutation, respectively.…”