Abstract
AbstractIn 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$
W
(
D
4
)
obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$
W
(
D
4
)
are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$
W
(
D
4
)
: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python.
Publisher
Springer Science and Business Media LLC
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