Orbit closures in the enhanced nilpotent cone

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• Pramod Achar (Louisiana State University and INI)
• Monday 23 February 2009, 16:00-17:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Anton Evseev.

Let $\mathcal N$ denote the set of $n \times n$ nilpotent matrices. The ``enhanced nilpotent cone’’ is the space $\mathbb C^n \times \mathcal N$. $GL(n)$ acts on $\mathbb C^n$ in an obvious way, and on $\mathcal N$ by conjugation. The orbits of this action are the subject of this talk. From this surprisingly elementary starting point, I will discuss connections to various topics in representation theory, combinatorics, and algebraic geometry, and especially to Syu Kato’s work on the ``exotic nilpotent cone’’ and affine Hecke algebras. This is joint work with A. Henderson.

This talk is part of the Junior Algebra and Number Theory seminar series.

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