Universal character factorisations

par Seamus Albion (Universität Wien)

mardi 28 févr. 2023, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux, Bât Braconnier (ICJ, Université Lyon 1)

An old result of Littlewood gives a factorisation for the Schur polynomial at a set of variables "twisted" by a primitive root of unity in terms of the core and quotient of the indexing partition. While somewhat neglected, Littlewood's formula has still found important applications in the representation theory of the symmetric group, plethysm, and much more. Recently, Ayyer and Kumari proved similar results for the characters of the symplectic and orthogonal groups. I will explain how all of these factorisations lift to the more general level of universal characters.