Séminaire SPACE Tours
# Deligne’s interpolation categories and modular symmetric functions

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Europe/Paris

E2 1180 (Tours)
### E2 1180

#### Tours

Description

In a seminal paper from 2004, Deligne introduced tensor

categories that interpolate the classical representation categories of

symmetric groups. These categories are described combinatorially using

partitions and are indexed by a complex number _t_. Deligne (for generic

_t_) and Comes-Ostrik (for general _t_) showed that indecomposable

objects of Deligne’s categories are parametrized by partitions of

arbitrary length. Moreover, the graded Grothendieck ring is isomorphic

to the ring of symmetric functions. In this talk, I will introduce and

motivate Deligne’s interpolation categories and explain techniques

used to classify indecomposable objects in these and more general

families of interpolation categories due to Khovanov-Sazdanov. In

particular, these techniques show that the graded Grothendieck ring of

characteristic _p_ analogues of Deligne’s categories is given by a

ring of modular symmetric functions. This talk is based on joint work

with Johannes Flake (Bonn) and Sebastian Posur (Münster).