### GRT at Home Seminar

**Curtis Wendlandt, Ohio State University**

*Poles of finite-dimensional representations of Yangians*

Organizer's time: 2021-04-13 17:00 Europe/Rome

Duration: 1 hour 15 minutes

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The Yangian associated to a complex simple Lie algebra g is a remarkable Hopf algebra whose representation theory provides an arena where algebra, analysis, geometry and mathematical physics all collide frequently. A finite-dimensional representation V of the Yangian is specified by a family of End(V)-valued rational functions of a single variable which satisfy certain commutation relations. In this talk, I will present a complete description of the poles of these rational functions which is valid whenever the underlying representation V is irreducible. Time permitting, I will highlight some applications of this result to various topics, including Baxter polynomials, denominator formulae for rational R-matrices, representations of the Yangian double, and cyclicity/irreducibility conditions for tensor products of simple modules. This is based on joint work with Sachin Gautam.

Submitted by: Andrea Appel