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 |
ASJC Scopus subject areas
- Mathematics(all)
- Gender Studies
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Cite this
Fishel, S. (2019). A Survey of the Shi Arrangement. In Association for Women in Mathematics Series (pp. 75-113). (Association for Women in Mathematics Series; Vol. 16). Springer. https://doi.org/10.1007/978-3-030-05141-9_3