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2015 Kazhdan Lusztig Cells in Infinite Coxeter Groups
M.V. Belolipetsky, P.E. Gunnells
J. Gen. Lie Theory Appl. 9(S1): 1-4 (2015). DOI: 10.4172/1736-4337.S1-002


Groups defined by presentations of the form $\langle s_1,\ldots,s_n | s_i^2 = 1, (s_is_j)^{m_{ij}} = 1(i,j=1,\ldots,n)\rangle$ are called Coxeter groups. The exponents $m_{i,j} ∈ N ∪ {∞}$ form the Coxeter matrix, which characterizes the group up to isomorphism. The Coxeter groups that are most important for applications are the Weyl groups and affine Weyl groups. For example, the symmetric group $S_n$ is isomorphic to the Coxeter group with presentation $\langle s_1,\ldots,s_n | s_i^2 = 1 (i=1,\ldots,n),(s_is_{i+1})^3=1(i=1,\ldots,n-1)\rangle$, and is also known as the Weyl group of type $A_{n-1}$.


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M.V. Belolipetsky. P.E. Gunnells. "Kazhdan Lusztig Cells in Infinite Coxeter Groups." J. Gen. Lie Theory Appl. 9 (S1) 1 - 4, 2015.


Published: 2015
First available in Project Euclid: 11 November 2016

zbMATH: 1372.20008
MathSciNet: MR3637846
Digital Object Identifier: 10.4172/1736-4337.S1-002

Keywords: Coxeter , hyperplane , Lusztig cells

Rights: Copyright © 2015 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.9 • No. S1 • 2015
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