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Journal of Lie Theory 32 (2022), No. 2, 499--518
Copyright Heldermann Verlag 2022

The Boundness and Lowest Two-Sided Cell of Weighted Coxeter Groups of Rank 3

Jianwei Gao
Beijing International Center for Mathematical Research, Peking University, P. R. China

We consider weighted Coxeter groups of rank 3 and its Hecke algebras in this paper. In this case, we show the boundness (in the sense of G. Lusztig) and the existence of a lowest two-sided cell c0. Then we describe c0 and the left cells in it. At last, we show that our conjectures P0--P15 hold for c0.

Keywords: Weighted Coxeter group, Hecke algebra, two-sided cell, left cell, A-function.

MSC: 20C08, 20F55.

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