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Plethystic vertex operators and boson-fermion correspondences

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2016

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Jarvis, Peter D
King, Ronald C

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https://doi.org/10.1088/1751-8113/49/42/425201
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Journal of Physics / A: Mathematical and Theoretical. 2016, 49(42), 425201. ISSN 1751-8113. eISSN 1751-8121. Available under: doi: 10.1088/1751-8113/49/42/425201

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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.

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ISO 690FAUSER, Bertfried, Peter D JARVIS, Ronald C KING, 2016. Plethystic vertex operators and boson-fermion correspondences. In: Journal of Physics / A: Mathematical and Theoretical. 2016, 49(42), 425201. ISSN 1751-8113. eISSN 1751-8121. Available under: doi: 10.1088/1751-8113/49/42/425201
BibTex
@article{Fauser2016-10-21Pleth-37443,
  year={2016},
  doi={10.1088/1751-8113/49/42/425201},
  title={Plethystic vertex operators and boson-fermion correspondences},
  number={42},
  volume={49},
  issn={1751-8113},
  journal={Journal of Physics / A: Mathematical and Theoretical},
  author={Fauser, Bertfried and Jarvis, Peter D and King, Ronald C},
  note={Article Number: 425201}
}
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