Journal of Lie Theory

no. 2
The Boundness and Lowest Two-Sided Cell of Weighted Coxeter Groups of Rank 3
Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 499-518
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.
DOI: 10.5802/jolt.1240
Classification: 20C08, 20F55
Keywords: Weighted Coxeter group, Hecke algebra, two-sided cell, left cell, A-function 
@article{JOLT_2022_32_2_a8,
     author = {J. Gao},
     title = {The {Boundness} and {Lowest} {Two-Sided} {Cell} of {Weighted} {Coxeter} {Groups} of {Rank} 3},
     journal = {Journal of Lie Theory},
     pages = {499--518},
     year = {2022},
     volume = {32},
     number = {2},
     doi = {10.5802/jolt.1240},
     zbl = {1529.20062},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1240/}
}
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J. Gao. The Boundness and Lowest Two-Sided Cell of Weighted Coxeter Groups of Rank 3. Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 499-518. doi: 10.5802/jolt.1240

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