Seminar on Combinatorics, Lie Theory, ​and Topology

On a quadratic polynomial attached to simple Lie algebras

by Paolo Papi (Sapienza Università di Roma)


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.