Lie Groups Seminar

Victor ProtsakCornell University
Representations of the infinite general Lie algebra are stranger than you may think

Friday, November 10, 2017 - 3:30pm
Malott 406

The Lie algebra of $\Bbb{N}\times\Bbb{N}$ finitary matrices is one of the most fundamental objects in infinite-dimensional Lie algebra theory. To some extent, the study of its structure and representations proceeds along the well-trodden route for the finite general linear Lie algebra $\mathfrak{gl}(n)$. We will explore connections to the finite case, find some natural analogues and uncover new phenomena within and just beyond the simplest class of "polynomial" representations, which require new insights and tools.