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Plethystic vertex operators and boson-fermion correspondences

Citation

Fauser, B and Jarvis, PD and King, RC, Plethystic vertex operators and boson-fermion correspondences, Journal of Physics A: Mathematical and Theoretical, 49, (42) Article 425201. ISSN 1751-8113 (2016) [Refereed Article]

Copyright Statement

Copyright 2016 IOP Publishing Ltd

DOI: doi:10.1088/1751-8113/49/42/425201

Abstract

We 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.

Item Details

Item Type:Refereed Article
Keywords:vertex operator, character ring, symmetric function, plethysm, Clifford algebra, free fermion
Research Division:Mathematical Sciences
Research Group:Mathematical Physics
Research Field:Algebraic Structures in Mathematical Physics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:115122
Year Published:2016
Deposited By:Mathematics and Physics
Deposited On:2017-03-08
Last Modified:2017-11-01
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