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JCT
2016

Chains in weak order posets associated to involutions

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Chains in weak order posets associated to involutions
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order posets of three different sets of involutions in the symmetric group, namely, the set of all involutions, the set of all fixed point free involutions, and the set of all involutions with signed fixed points (or “clans”). These distinguished sets of involutions parameterize Borel orbits in the classical symmetric spaces associated to the general linear group. In particular, we give a complete characterization of the maximal chains of an arbitrary lower order ideal in any of these three posets.
Mahir Bilen Can, Michael Joyce, Benjamin Wyser
Added 06 Apr 2016
Updated 06 Apr 2016
Type Journal
Year 2016
Where JCT
Authors Mahir Bilen Can, Michael Joyce, Benjamin Wyser
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