TY - CHAP
T1 - A Survey of the Shi Arrangement
AU - Fishel, Susanna
PY - 2019
Y1 - 2019
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.
UR - http://www.scopus.com/inward/record.url?scp=85071492168&partnerID=8YFLogxK
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 -