Plethystic vertex operators and boson-fermion correspondences
Plethystic vertex operators and boson-fermion correspondences
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2016
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Journal of Physics / A: Mathematical and Theoretical ; 49 (2016), 42. - 425201. - ISSN 1751-8113. - eISSN 1751-8121
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.
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FAUSER, Bertfried, Peter D JARVIS, Ronald C KING, 2016. Plethystic vertex operators and boson-fermion correspondences. In: Journal of Physics / A: Mathematical and Theoretical. 49(42), 425201. ISSN 1751-8113. eISSN 1751-8121. Available under: doi: 10.1088/1751-8113/49/42/425201BibTex
@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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