Corpus ID: 237581547

Kazhdan--Lusztig cells of $\mathbf{a}$-value 2 in $\mathbf{a}(2)$-finite Coxeter systems

  title={Kazhdan--Lusztig cells of \$\mathbf\{a\}\$-value 2 in \$\mathbf\{a\}(2)\$-finite Coxeter systems},
  author={R. M. Green and Tianyuan Xu},
  • R. Green, Tianyuan Xu
  • Published 20 September 2021
  • Mathematics
A Coxeter group is said to be a(2)-finite if it has finitely many elements of a-value 2 in the sense of Lusztig. 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… Expand


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