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q-difference intertwining operators for $U_q(sl(n))$: general setting and the case $n=3$

V. K. Dobrev
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Abstract

We construct representations $\hatπ_{\br}$ of the quantum algebra $U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of formal power series of $n(n-1)/2$ non-commuting variables. These variables generate a flag manifold of the matrix quantum group $SL_q(n)$ which is dual to $U_q(sl(n))$. The conditions for reducibility of $\hatπ_{\br}$ and the procedure for the construction of the $q$ - difference intertwining operators are given. The representations and $q$ - difference intertwining operators are given in the most explicit form for $n=3$. In the Note Added some general results for arbitrary $n$ are given.

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V. K. Dobrev. 2003-12-15. q-difference intertwining operators for $U_q(sl(n))$: general setting and the case $n=3$. https://doi.org/10.1088/0305-4470%2F27%2F14%2F013

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