Speaker: **Sutanu Roy** (NISER)

Title: Contraction and bosonisation

Time/Date: 4:45-6:15pm, November 12 (Thu.), 2020

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract: In 1953 Inönü and Wigner introduced *group contraction*: a systematic (limiting)
process to obtain from a given Lie group a non-isomorphic Lie group. For example, the
contraction of SU(2) group (with respect to its closed subgroup T) is isomorphic to the
double cover of E(2) group. The q-deformed C^{*}-algebraic analogue of this example was
introduced and investigated by Woronowicz during the mid '80s to early '90s. More precisely,
the C^{*}-algebraic deformations of SU(2) and (the double cover of) E(2) with respect to real
deformation parameters 0 < |q| < 1 become compact (denoted by SU_{q}(2)) and non-compact
locally compact (denoted by E_{q}(2)) quantum groups, respectively. Furthermore, the
contraction of SU_{q}(2) groups becomes (isomorphic) to E_{q}(2) groups. However, for complex
deformation parameters 0 < |q| < 1, the objects SU_{q}(2) and E_{q}(2) are not ordinary but
braided quantum groups. More generally, the quantum analogue of the normal subgroup
of a semidirect product group becomes a braided quantum group and the reconstruction
process of the semidirect product quantum group from a braided quantum group is called
bosonisation. In this talk, we shall present a braided version of the contraction
procedure between SU_{q}(2) and E_{q}(2) groups (for complex deformation parameters 0 < |q| < 1)
and address its compatibility with bosonisation.
This is based on a joint work with Atibur Rahaman.