Simple-root bases for Shi arrangements

Takuro Abe, Hiroaki Terao

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, we know very little about the bases themselves except their existence. In this article, we prove the unique existence of two distinguished bases which we call the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-). They are characterized by nice divisibility properties relative to the simple roots.

Original languageEnglish
Pages (from-to)89-104
Number of pages16
JournalJournal of Algebra
Volume422
DOIs
Publication statusPublished - Jan 5 2015

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Arrangement
Roots
Module
Divisibility
Logarithmic
Cone

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Simple-root bases for Shi arrangements. / Abe, Takuro; Terao, Hiroaki.

In: Journal of Algebra, Vol. 422, 05.01.2015, p. 89-104.

Research output: Contribution to journalArticle

Abe, Takuro ; Terao, Hiroaki. / Simple-root bases for Shi arrangements. In: Journal of Algebra. 2015 ; Vol. 422. pp. 89-104.
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