Combinatorial Fock space and representations of quantum groups at roots of unity

28.05.2019 13:15 - 14:45

Martina Lanini, Università di Roma "Tor Vergata"

Abstract:   The classical Fock space arises in the context of
mathematical physics, where one would like to describe the behaviour of
certain configurations with an unknown number of identical,
non-interacting particles. By work of Leclerc and Thibon, (its
q-analogue) has a realisation in terms of the affine Hecke algebra of
type A and it controls the representation theory of the corresponding
quantum group at a root of unity. In joint work with Arun Ram and Paul
Sobaje, we produce a generalisation of the q-Fock space to all Lie
types. This gadget can also be realised in terms of affine Hecke algebra
and captures decomposition numbers for quantum groups at roots of unity.

Organiser:

H. Grobner, A. Minguez-Espallargas, A. Mellit

Location:

BZ 9, 9. OG, OMP1