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You searched for subject:(Kazhdan Lusztig Cells). One record found.

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University of Colorado

1. Gern, Tyson Charles. Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D.

Degree: PhD, Mathematics, 2013, University of Colorado

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. Advisors/Committee Members: Richard M. Green, Nathaniel Thiem, Martin Walter, Stephen Doty, James M. Douglass.

Subjects/Keywords: Algebraic Combinatorics; Coxeter Groups; Domino Tableaux; Kazhdan-Lusztig Cells; Kazhdan-Lusztig Polynomials; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gern, T. C. (2013). Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/26

Chicago Manual of Style (16th Edition):

Gern, Tyson Charles. “Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D.” 2013. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/26.

MLA Handbook (7th Edition):

Gern, Tyson Charles. “Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D.” 2013. Web. 30 Oct 2020.

Vancouver:

Gern TC. Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2020 Oct 30]. Available from: https://scholar.colorado.edu/math_gradetds/26.

Council of Science Editors:

Gern TC. Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/math_gradetds/26

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