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

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

1994-05-24

arxiv.org/abs/hep-th/9405150v2

J.Phys. A27 (1994) 4841-4858; Addendum-ibid. A27 (1994) 6633-6634

Physics

High Energy Physics

High Energy Physics - Theory

24 pages; v2 includes Note Added published in J.Phys. A27 (1994), references updated

Scientific paper

10.1088/0305-4470/27/14/013

We construct representations $\hat\pi_{\br}$ 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 $\hat\pi_{\br}$ 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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