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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

URL: https://scholar.colorado.edu/math_gradetds/26

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 P_{x,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 (6^{th} 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 (16^{th} Edition):

Gern, Tyson Charles. “Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D.” 2013. Doctoral Dissertation, University of Colorado. Accessed October 28, 2020. https://scholar.colorado.edu/math_gradetds/26.

MLA Handbook (7^{th} Edition):

Gern, Tyson Charles. “Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D.” 2013. Web. 28 Oct 2020.

Vancouver:

Gern TC. Leading Coefficients of Kazhdan–Lusztig Polynomials in Type D. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2020 Oct 28]. 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