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Leading Coefficients of Kazhdan--Lus...

Gern, Tyson Charles.

Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D.
Author:	Gern, Tyson Charles.
Description:	95 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Notes:	Adviser: Richard M. Green.
Contained By:	Dissertation Abstracts International74-09B(E).
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3561962
ISBN:	9781303093746

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

Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D. - 95 p.

Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.

Thesis (Ph.D.)--University of Colorado at Boulder, 2013.

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, mu(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 mu-value computation difficult.

ISBN: 9781303093746Subjects--Topical Terms:

184409
Mathematics.

Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D.
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020 $a 9781303093746
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100 1 $a Gern, Tyson Charles. $3 660284
245 1 0 $a Leading Coefficients of Kazhdan--Lusztig Polynomials in Type D.
300 $a 95 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
500 $a Adviser: Richard M. Green.
502 $a Thesis (Ph.D.)--University of Colorado at Boulder, 2013.
520 $a 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, mu(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 mu-value computation difficult.
520 $a 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 mu-values involving bad elements. I will conclude by showing that mu(x, w ) is 0 or 1 when x is fully commutative in type D..
590 $a School code: 0051.
650 4 $a Mathematics. $3 184409
650 4 $a Applied Mathematics. $3 530992
690 $a 0405
690 $a 0364
710 2 $a University of Colorado at Boulder. $b Mathematics. $3 660285
773 0 $t Dissertation Abstracts International $g 74-09B(E).
790 $a 0051
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3561962

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