Abstract
Let w ↦ ( P ( w ) , Q ( w ) ) be the Robinson-Schensted correspondence between the symmetric group S n and the set of pairs of standard tableaux with the same shapes. We show that each Kazhdan-Lusztig basis (KL basis for short) element C ′ w can be expressed as a linear combination of some f s t which satisfies that s ¥ P ( w ) ∗ , t ¥ Q ( w ) ∗ , where “ ¥ ” is the dominance (partial) order between standard tableaux, u ∗ denotes the conjugate of u for each standard tableau u , { f s t | s , t ∈ Std ( λ ) , λ⊢n } is the seminormal basis of the Iwahori-Hecke algebra associated to S n . As a result, we generalize an earlier result of Geck on the relation between the KL basis and the Murphy basis. Similar relations between the twisted KL basis, the dual seminormal basis and the dual Murphy basis are obtained.
Published Version
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