Computes minimally dominant elements and the intersections of their Bruhat cells with conjugacy classes, as described in this paper.
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This repository contains two files:
Computes dominant and minimally dominant elements in a Weyl group. In particular, it provides a function which computes for each (nontrivial and nonelliptic) conjugacy class in such a group a pair of elements - one of minimal length and one which is minimally dominant. These are returned as reduced words following GAP notation.
Written for SageMath version 8.7 and tested with 9.4, using Python 3.9.5.
Uses such pairs of elements to test whether the corresponding Bruhat cells intersect the same conjugacy classes in the associated simply connected reductive group.
Written for (Jean Michel's Julia port of) Gapjm. Tested with commit 5728d89, using Julia 1.7.0-rc1.
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More details and sample inputs are provided in both files.