Induction

Lars Tuset
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Lars Tuset: Oslo Metropolitan University, Department of Computer Science

Chapter Chapter 20 in Analysis and Quantum Groups, 2022, pp 539-545 from Springer

Abstract: Abstract Let (W2, Δ2) be a locally compact quantum group with a locally compact quantum subgroup (W1, Δ1), and let L be a unitary corepresentation of the latter, meaning that L ∈ W 1 ⊗ ̄ B ( V ) $$L\in W_1\bar \otimes B(V)$$ is unitary and ( Δ1 ⊗ ι)(L) = L13L23, where V is a Hilbert space. Then we define the so called induced corepresentation M(L) of L, and do indeed prove, using modular theory, that M(L) is a unitary corepresentation of (W2, Δ2) on a larger Hilbert space; a construction that reduces to a well known one in the classical situation of a unitary representation of a subgroup of a group.

Date: 2022
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DOI: 10.1007/978-3-031-07246-8_20

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