Comital Ireland, 1333–1534

The history of late-medieval Ireland is not exactly littered with dates that command general recognition, so it is surely suggestive that two which have achieved a degree of notoriety concern the fortunes, or rather misfortunes, of Ireland’s earls and earldoms: the murder of William Burgh, the ‘brown’ earl of Ulster, in 1333; and the rebellion in 1534 of Thomas Fitzgerald (‘Silken Thomas’), soon-to-be tenth earl of Kildare. These are dates of demarcation. In the broadest terms, 1333 has been understood to mark the end of the expansion of royal power under the Plantagenets, 1534 the start of its vigorous reassertion under the Tudors. What occurred between these chronological bookends? For Goddard Orpen (d. 1932), writing in 1920 when the Anglo-Irish tradition he cherished seemed imperilled by the prospect of Irish secession from the United Kingdom, the murder of the earl of Ulster in 1333 was a moment of dark, almost metonymic, significance: ‘the door was now closed on a century and a half of remarkable progress, vigour, and comparative order, and two centuries of retrogression, stagnation, and comparative anarchy were about to be ushered in’

The Torus-Equivariant Cohomology of Nilpotent Orbits

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the action of a maximal compact torus of the overall group in question.Comment: 17 pages. Comments are most welcome. Version 2: A few minor changes were mad

On Projective Equivalence of Univariate Polynomial Subspaces

We pose and solve the equivalence problem for subspaces of ${\mathcal P}_n$, the $(n+1)$ dimensional vector space of univariate polynomials of degree $\leq n$. The group of interest is ${\rm SL}_2$ acting by projective transformations on the Grassmannian variety ${\mathcal G}_k{\mathcal P}_n$ of $k$-dimensional subspaces. We establish the equivariance of the Wronski map and use this map to reduce the subspace equivalence problem to the equivalence problem for binary forms