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Vertex Operators Arising from Jacobi–Trudi Identities

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Abstract

We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi–Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi–Trudi identity the action of a Clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions. A generalized Giambelli identity is also proved to follow from that identity. As applications, we obtain explicit formulas for vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  2. Department of Mathematics, Kansas State University, Manhattan, KS, 66502, USA

    Natasha Rozhkovskaya

Authors
  1. Naihuan Jing
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  2. Natasha Rozhkovskaya
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Correspondence to Natasha Rozhkovskaya.

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Communicated by A. Borodin

Supported in part by Simons Foundation and NSFC.

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Jing, N., Rozhkovskaya, N. Vertex Operators Arising from Jacobi–Trudi Identities. Commun. Math. Phys. 346, 679–701 (2016). https://doi.org/10.1007/s00220-015-2564-9

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  • DOI: https://doi.org/10.1007/s00220-015-2564-9

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