On a quadratic polynomial attached to simple Lie algebras – Paolo Papi (Sapienza Università di Roma)

Abstract

We will introduce a polynomial $p_{\mathfrak{g}}(k)$ attached to a simple Lie algebra $\mathfrak{g}$. It appears in several different contexts:

1. the minimal quantization of the adjoint representation of Drinfeld’s Yangian $\mathsf{Y}(\mathfrak{g})$;
2. the generating relations for the minimal $W(\mathfrak{g})$;
3. unitarity problems for minimal W-algebras.

After giving the setup for (1), (2), (3), we will provide an explanation of a surprising coincidence regarding (1), (2); then we will discuss the role of $p_{\mathfrak{g}}(k)$ in (3).
The results pertain to joint projects with Kac and Moseneder Frajria.

Click here to see the slides of the talk and here to see the video of the talk.

Further information is available on the event page on the Indico platform.