TY - CHAP

T1 - A Survey of the Shi Arrangement

AU - Fishel, Susanna

PY - 2019

Y1 - 2019

N2 - In [58], Shi proved Lusztigâ€™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 Lusztigâ€™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 -