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Plethystic vertex operators and boson-fermion correspondences
journal contribution
posted on 2023-05-19, 02:57 authored by Fauser, B, Peter JarvisPeter Jarvis, King, RCWe study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.
History
Publication title
Journal of Physics A: Mathematical and TheoreticalVolume
49Issue
42Article number
425201Number
425201Pagination
1-24ISSN
1751-8113Department/School
School of Natural SciencesPublisher
Institute of Physics Publishing Ltd.Place of publication
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