A Survey of the Shi Arrangement

Susanna Fishel

doi:10.1007/978-3-030-05141-9_3

A Survey of the Shi Arrangement

Susanna Fishel

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In [58], Shi proved Lusztigâ€™s conjecture that the number of two-sided cells for the affine Weyl group of type A_n-1 is the number of partitions of n. As a byproduct, he introduced the Shi arrangement of hyperplanes and found a few of its remarkable properties. The Shi arrangement has since become a central object in algebraic combinatorics. This article is intended to be a fairly gentle introduction to the Shi arrangement, intended for readers with a modest background in combinatorics, algebra, and Euclidean geometry.

Original language	English (US)
Title of host publication	Association for Women in Mathematics Series
Publisher	Springer
Pages	75-113
Number of pages	39
DOIs	https://doi.org/10.1007/978-3-030-05141-9_3
State	Published - 2019

Publication series

Name	Association for Women in Mathematics Series
Volume	16
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

ASJC Scopus subject areas

Mathematics(all)
Gender Studies

Access to Document

10.1007/978-3-030-05141-9_3

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