Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})]$ revisited

Abstract

In a previous paper the generator matrix elements and (dual) vector reduced Wigner coefficients (RWCs) were evaluated via the polynomial identities satisfied by a certain matrix constructed from the $R$-matrix $R$ and its twisted counterpart $R^T=T\circ R$. Here we provide an alternative evaluation utilising the $R$-matrix $\tilde{R}=(R^T{)}^{-1}$. This provides a new direct derivation of the vector RWCs obtained indirectly in earlier work via a symmetry relation. This approach has the advantage that it generalises to the Lie superalgebra case, which will be investigated elsewhere.

52 pages

References in corpus (6)

• Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)
• Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
• Characteristic identities for Lie (super)algebras
• Reduced matrix elements of the orthosymplectic Lie superalgebra
• Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
• Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

Cited by in corpus (1)

• Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras