Fully commutative elements of the complex reflection groups

Gabriel Feinberg; Sungsoon Kim; Kyu Hwan Lee; Se jin Oh

doi:10.1016/j.jalgebra.2019.04.026

Fully commutative elements of the complex reflection groups

Gabriel Feinberg, Sungsoon Kim, Kyu Hwan Lee, Se jin Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.

Original language	English
Pages (from-to)	371-394
Number of pages	24
Journal	Journal of Algebra
Volume	558
DOIs	https://doi.org/10.1016/j.jalgebra.2019.04.026
State	Published - 15 Sep 2020

Keywords

Catalan Triangle
Catalan numbers
Complex reflection groups
Fully commutative elements

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10.1016/j.jalgebra.2019.04.026

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title = "Fully commutative elements of the complex reflection groups",

abstract = "We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.",

keywords = "Catalan Triangle, Catalan numbers, Complex reflection groups, Fully commutative elements",

author = "Gabriel Feinberg and Sungsoon Kim and Lee, {Kyu Hwan} and Oh, {Se jin}",

note = "Funding Information: This work was partially supported by a grant from the Simons Foundation (#318706).This work was partially supported by the National Research Foundation of Korea (NRF-2016R1C1B2013135). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - Lee, Kyu Hwan

AU - Oh, Se jin

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PY - 2020/9/15

Y1 - 2020/9/15

N2 - We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.

AB - We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.

KW - Catalan Triangle

KW - Catalan numbers

KW - Complex reflection groups

KW - Fully commutative elements

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DO - 10.1016/j.jalgebra.2019.04.026

M3 - Article

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SN - 0021-8693

VL - 558

SP - 371

EP - 394

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Fully commutative elements of the complex reflection groups

Abstract

Keywords

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