## Workshop

Notizie sull'evento al link: https://sites.google.com/a/uniroma1.it/stefanocapparelli-eng/workshop-2023

Il workshop prevede un lavoro di laboratorio matematico tra i partecipanti e tre incontri di tipo generale per un pubblico piu' ampio, secondo il seguente calendario

*Groebner basis approach to combinatorial bases of standard modules for affine Lie algebras*

Abstract:

I'll describe the "Groebner basis approach" used in the joint works with A. Meurman on

combinatorial bases of standard modules for A_1^(1) and on A_2^(1), and comment on the advantages and drawbacks of this approach in general. If time permits, I'll comment on some technical differences that appear in I. Siladić's work on A_2^(2).

Wednesday, May 24th, 15.00, room 1B1

### Tomislav Šikić, University of Zagreb

*Combinatorial relations among relations for standard $C^{(1)}_n$-modules of level 2,3,…?*

Abstract:

Title: Integer partitions and characters of affine Lie algebras

A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. In the 1980's, Lepowsky and Wilson established a connection between the Rogers-Ramanujan partition identities and characters of affine Lie algebras. Since then, a nice interplay between combinatorics and representation theory has led to the discovery of new results in both fields. After presenting the history of these interactions, we will introduce grounded partitions, a generalisation of partitions which is well-suited for a connection with representation theory, and show how they can be used to prove partition identities and character formulas.