On Matrix Quantum Groups of type $A_n$

Details On Matrix Quantum Groups of type $A_n$ On Matrix Quantum Groups of type $A_n$

1997-08-05

arxiv.org/abs/q-alg/9708007v3

Mathematics

Quantum Algebra

Ams-Latex file, 26 pages, bezier style, use style file grcalc.sty

Scientific paper

Given a Hecke symmetry $R$, one can define a matrix bialgebra $E_R$ and a matrix Hopf algebra $H_R$, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to $R$. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend only on the rank of the Hecke symmetry. Further we compute the quantum rank of simple representations. We also show that the quantum semi-group is ``Zariski'' dense in the quantum group. Finally we give a formula for the integral.

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