Algebra Seminar

Erich Jauch
An Alternating Analogue of $U(\mathfrak{gl}_n)$ and Its Representations

The universal enveloping algebra of a Lie algebra $\mathfrak{g}$ is of utmost importance when studying representations of $\mathfrak{g}$. In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times S_2\times\cdots\times S_n$ where $S_j$ is the symmetric group on $j$ variables. With some connections to Galois Theory, an interesting question is what would a similar object be in the invariant ring with respect to a product of Alternating groups? We will discuss such an object and some results about its representations and how they relate to $U(\mathfrak{gl}_n)$ representations. This is based on the work in my recent preprint arXiv:1907.13254

Event Date: 
October 21, 2019 - 3:30pm to 4:20pm
217 MLH
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