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.
Combinatorial Fock space and representations of quantum groups at roots of unity
28.05.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: