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Title: Frobenius structures, Coxeter discriminants, and supersymmetric mechanics
Author: Antoniou, Georgios
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 2020
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This thesis contains two directions both related to Frobenius manifolds. In the first part we deal with the orbit space M_W = V/W of a finite Coxeter group W acting in its reflection representation V. The orbit space M_W carries the structure of a Frobenius manifold and admits a pencil of flat metrics of which the Saito flat metric η, defined as the Lie derivative of the W-invariant form g on V is the key object. In the main result of the first part we find the determinant of Saito metric restricted on the Coxeter discriminant strata in M_W . It is shown that this determinant in the flat coordinates of the form g is proportional to a product of linear factors. We also find multiplicities of these factors in terms of Coxeter geometry of the stratum. In the second part we study N = 4 supersymmetric extensions of quantum mechanical systems of Calogero–Moser type. We show that for any ∨-system, in particular, for any Coxeter root system, the corresponding Hamiltonian can be extended to the supersymmetric Hamiltonian with D(2,1;α) symmetry. We also obtain N = 4 supersymmetric extensions of Calogero–Moser–Sutherland systems. Thus, we construct supersymmetric Hamiltonians for the root systems BC_N, F_4 and G_2.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics