Abstract
In [58], Shi proved Lusztig’s conjecture that the number of two-sided cells for the affine Weyl group of type An-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 | |
| State | Published - Jan 1 2019 |
Publication series
| Name | Association for Women in Mathematics Series |
|---|---|
| Volume | 16 |
| ISSN (Print) | 2364-5733 |
| ISSN (Electronic) | 2364-5741 |
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ASJC Scopus subject areas
- Mathematics(all)
- Gender Studies
Cite this
A Survey of the Shi Arrangement. / Fishel, Susanna.
Association for Women in Mathematics Series. Springer, 2019. p. 75-113 (Association for Women in Mathematics Series; Vol. 16).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - A Survey of the Shi Arrangement
AU - Fishel, Susanna
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In [58], Shi proved Lusztig’s conjecture that the number of two-sided cells for the affine Weyl group of type An-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.
AB - In [58], Shi proved Lusztig’s conjecture that the number of two-sided cells for the affine Weyl group of type An-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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85071492168&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-05141-9_3
DO - 10.1007/978-3-030-05141-9_3
M3 - Chapter
AN - SCOPUS:85071492168
T3 - Association for Women in Mathematics Series
SP - 75
EP - 113
BT - Association for Women in Mathematics Series
PB - Springer
ER -