# Events

# Workshop Representation Theory and Integrability on the occasion of Kayed Al Qasimi’s Ph.D. defence

**Program April 17th, 2019**

**14:00-14:45:** Christian Korff (Univ. of Glasgow).

**Title:** The asymmetric six-vertex model, cylindric symmetric functions and virtual Hecke characters.

**Abstract:** The asymmetric six-vertex model describes ice and other ferroelectrics on a square lattice. In this talk we will use it in the infinite lattice limit as a combinatorial tool to describe Hecke characters of irreducible finite-dimensional modules. More precisely, we show that on the infinite square lattice a Hecke version of the celebrated boson-fermion correspondence “diagonalises” the transfer matrix. When specialising to periodic boundary conditions we show that one obtains from the six-vertex partition function on the infinite cylinder so-called cylindric symmetric functions whose expansions into monomials give rise to virtual Hecke characters. These virtual characters span an infinite-dimensional subcoalgebra in the Grothendieck ring of Hecke algebras with respect to the restriction functor. The structure constants of the subcoalgebra are the Gromov-Witten invariants of Grassmannians.

**15:00-15:45:** Jesper Jacobsen (École Normale Supérieure & Sorbonne Université).

**Title:** TBA

**Abstract:** TBA

**16:00-16:45:** Nicolai Reshetikhin (University of California, Berkeley & UvA).

**Title:** The statistics of irreducible components in large tensor products of finite dimensional representations of simple Lie algebras.

**Abstract:** The probability distribution of irreducible subrepresentations is computed for tensor products $\otimes_k V_k^{\otimes N_k}$ in the limit when $N_k\to \infty$ while $N_1:N_2:\sdots N_m$ remain finite.

For the character distribution, where the probability is proportional to the multiplicity of the irreducible representation time its charter computed at $e^t$ where $t$ is an element of principle Weyl chamber, the asymptotical distribution is universal and depends only on the stabilizer of $t$ in the Weyl group, i.e. whether $t$ is inside the Weyl chamber or on a startup of its boundary.

This is a joint work with O. Postnova and V. Serganova.

We cordially invite you to attend!

**Program April 18th**

**10:00 (Agnietenkapel, Oudezijds Voorburgwal 231, Amsterdam)**

Kayed Al Qasimi’s PhD defence of the thesis entitled “An elevator ride with Knizhnik and Zamolodchikov”.

You are also most welcome to attend the defence.

**Organizers:** Kayed Al Qasimi, Bernard Nienhuis and Jasper Stokman.