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arXiv · 1811.00229

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

Mark D. Gould·Phillip S. Isaac
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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.

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Mark D. Gould, Phillip S. Isaac. 2018-11-01. Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})]$ revisited. https://doi.org/10.1088/1751-8121%2Fab2676

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