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Type-I Quantum Superalgebras, $q$-Supertrace and Two-variable Link Polynomials

Mark D. Gould·Jon R. Links·Yao-Zhong Zhang
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Abstract

A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with {\em any} finite dimensional unitary irrep for these algebras. This affords a systematic construction of new two-variable link polynomials asociated with any finite dimensional irrep (with a real highest weight) for the type-I quantum superalgebras. In particular infinite families of non-equivalent two-variable link polynomials are determined in fully explicit form.

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Mark D. Gould, Jon R. Links, Yao-Zhong Zhang. 1995-10-09. Type-I Quantum Superalgebras, $q$-Supertrace and Two-variable Link Polynomials. https://doi.org/10.1063/1.531422

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