Graduate Thesis Or Dissertation
Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D Público Deposited
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Kazhdan–Lusztig polynomials arise in the context of Hecke algebras associated to Coxeter groups. The computation of these polynomials is very difficult for examples of even moderate rank. In type A it is known that the leading coefficient, μ(x, w) of a Kazhdan–Lusztig polynomial Px,w is either 0 or 1 when x is fully commutative and w is arbitrary. In type D Coxeter groups there are certain "bad" elements that make μ-value computation difficult.
The Robinson–Schensted correspondence between the symmetric group and pairs of standard Young tableaux gives rise to a way to compute cells of Coxeter groups of type A. A lesser known correspondence exists for signed permutations and pairs of so-called domino tableaux, which allows us to compute cells in Coxeter groups of types B and D. I will use this correspondence in type D to compute μ-values involving bad elements. I will conclude by showing that μ(x, w) is 0 or 1 when x is fully commutative in type D.
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- 2013
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- 2020-01-21
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Miniatura | Título | Fecha de subida | Visibilidad | Acciones |
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leadingCoefficientsOfKazhdanLusztigPolynomialsInTypeD.pdf | 2019-11-11 | Público | Descargar |