Representations of the Complex Classical Cayley-Klein Categories

Details Representations of the Complex Classical Cayley-Klein Categories Representations of the Complex Classical Cayley-Klein Categories

2006-10-28

arxiv.org/abs/math/0610877v1

Hadronic Journal Supplement, Vol. 18 No. 1, pp. 25-82(2003)

Mathematics

General Mathematics

58 pages, LaTex, no figures

Scientific paper

Complex classical Cayley-Klein categories ${\bf A({\bj})}$, ${\bf B({\bj})}$, ${\bf C({\bj})}$ and ${\bf D({\bj})}$ are constructed by the method of categorical extension of the complex classical Cayley-Klein groups $SL(2n;{\bj};{\Bbb C}), SO(2n+1;{\bj};{\Bbb C}), Sp(2n;{\bj};{\Bbb C})$ and $SO(2n;{\bj};{\Bbb C})$, respectively. The explicit construction of the irreducible representations of the complex classical Cayley-Klein categories is received. Completeness of lists of the irreducible representations of the complex classical Cayley-Klein categories and the classification theorems are proved.

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