Generalized reflection root systems

Maria Gorelik; Ary Shaviv

doi:10.1016/j.jalgebra.2017.08.010

Generalized reflection root systems

Maria Gorelik, Ary Shaviv

Department of Mathematics

Weizmann Institute of Science

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

Abstract

We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.

Original language	English
Pages (from-to)	490-516
Number of pages	27
Journal	Journal of Algebra
Volume	491
DOIs	https://doi.org/10.1016/j.jalgebra.2017.08.010
State	Published - 1 Dec 2017

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2017.08.010

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title = "Generalized reflection root systems",

abstract = "We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.",

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AB - We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.

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DO - 10.1016/j.jalgebra.2017.08.010

M3 - مقالة

SN - 0021-8693

VL - 491

SP - 490

EP - 516

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Generalized reflection root systems

Abstract

All Science Journal Classification (ASJC) codes

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