TY - CHAP
T1 - A Survey of the Shi Arrangement
AU - Fishel, Susanna
N1 - Funding Information:
Acknowledgements The author would like to thank Hélène Barcelo, Gizem Karaali, and Rosa Orellana for allowing her to write an article for this AWM series. She would like to thank Matthew Fayers, Sarah Mason, and Jian-Yi Shi for comments on the manuscript, and Nathan Williams and Brendon Rhoades for suggesting several related papers. She would like to thank Patrick Headley for help with his thesis. The anonymous referees’ comments helped enormously to improve exposition. This work was supported by a grant from the Simons Foundation (#359602, Susanna Fishel).
Publisher Copyright:
© 2019, The Author(s) and the Association for Women in Mathematics.
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.
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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 -