Factorization of Kazhdan–Lusztig elements for Grassmanians
نویسندگان
چکیده
We show that the Kazhdan-Lusztig basis elements Cw of the Hecke algebra of the symmetric group, when w ∈ Sn corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form Ti + fj(v), where fj are rational functions.
منابع مشابه
On the Dual Canonical and Kazhdan-lusztig Bases and 3412, 4231-avoiding Permutations
Using Du’s characterization of the dual canonical basis of the coordinate ring O(GL(n,C)), we express all elements of this basis in terms of immanants. We then give a new factorization of permutations w avoiding the patterns 3412 and 4231, which in turn yields a factorization of the corresponding Kazhdan-Lusztig basis elements C w(q) of the Hecke algebra Hn(q). Using the immanant and factorizat...
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