Quantum Lunch: Reality of Temperley-Lieb Hamiltonian spectra – University of Copenhagen

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Quantum Lunch: Reality of Temperley-Lieb Hamiltonian spectra

Speaker: Jørgen Rasmussen, University of Queensland.

Abstract: Using a diagrammatic approach, we describe the Temperley-Lieb algebras and some of their representations. Particular algebra elements correspond to Hamiltonians in a range of applications, and the reality of their spectra was conjectured many years ago. However, a proof remained elusive until very recently. Our proof is based on the construction, on each so-called standard module, of a new inner product with respect to which the associated Hamiltonian is self-adjoint.