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

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.

the version to be published in J. Math. Phys

References in corpus (3)

• A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
• On Type-I Quantum Affine Superalgebras
• Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: $U_q(gl(m|n))$}

Cited by in corpus (7)

• The Alexander polynomial as quantum invariant of links
• Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras
• Infinitely many two-variable generalisations of the Alexander-Conway polynomial
• Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariants
• Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)]
• Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras
• Four Easy Pieces - Explicit R Matrices from the (\dot{0}_m|α) Highest Weight Representations of U_q[gl(m|1)]