A Root System Criterion for Fully Commutative and Short Braid-Avoiding Elements in Affine Weyl Groups
Paola Cellini
and Paolo Papi
DOI: 10.1023/A:1008717502373
Abstract
We provide simple characterizations of short-braid avoiding and fully commutative elements in an affine Weyl group W, generalizing results of Fan and Stembridge for finite Weyl groups. Our results rely on the combinatorics of the compatible subsets of the root system of W.
Pages: 5–16
Keywords: affine Weyl group; short-braid avoiding element; fully commutative element
Full Text: PDF
References
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2. M. Dyer, “Hecke algebras and shellings of Bruhat intervals,” Comp. Math. 89 (1993), 91-115
3. C.K. Fan, “A Hecke Algebra Quotient and Properties of Commutative Elements of a Weyl Group,” MIT Thesis, 1995.
4. C.K. Fan, “Schubert varieties and short braidedness,” Transformation Groups 3 (1998), 51-57.
5. C.K. Fan and J.R. Stembridge, “Nilpotent orbits and commutative elements,” J. Alg. 196 (1997), 490-498.
6. V.G. Kac, Infinite Dimensional Lie Algebras, Birkh\ddot auser, Boston, 1983.
7. P. Papi, “A characterization of a special ordering in a root system,” Proc. Amer. Math. Soc. 120 (1994), 661-665.
8. J. Stembridge, “On the fully commutative elements of a Coxeter group,” J. Alg. Combin. 5 (1996), 353-385.