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.