On the dual canonical and Kazhdan-Lusztig bases and 3412-, 4231-avoiding permutations |
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Authors: | Mark Skandera |
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Institution: | Department of Mathematics, Lehigh University, Christmas-Saucon Hall, 14 East Packer Ave., Bethlehem, PA 18015, United States |
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Abstract: | 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 of the Hecke algebra Hn(q). Using the immanant and factorization results, we show that for every totally nonnegative immanant and its expansion with respect to the basis of Kazhdan-Lusztig immanants, the coefficient dw must be nonnegative when w avoids the patterns 3412 and 4231. |
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Keywords: | 05E05 15A15 20C08 20G42 |
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