Kazhdan–Lusztig cells of a -value 2 in a ( 2 ) -finite Coxeter systems
R. M. Green, Tianyuan Xu
Source abstract
A Coxeter group is said to be a ( 2 ) -finite if it has finitely many elements of a -value (in the sense of Lusztig) equal to 2. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided Kazhdan–Lusztig cells of a -value 2 in an irreducible a ( 2 ) -finite Coxeter group. In particular, we introduce elements we call stubs to parameterize the one-sided cells and we characterize the one-sided cells via both star operations and weak Bruhat orders. We also compute the cardinalities of all the one-sided and two-sided cells of a -value 2 in irreducible a ( 2 ) -finite Coxeter groups.
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