Applications to the Known Cyclic q-Clans

Abstract

To obtain the canonical form of the classical q-clan put k = m = 1 in Eqs. (4.7) and (4.8). A simple computation shows that if $w = \frac{1} {{\delta \frac{1} {2}}}$ , so tr(w) = 1, then the classical q-clan C in 1/2-normalized form is given by

$$ C = \left\{ {A_t = \left( {\begin{array}{*{20}c} {wt^{\tfrac{1} {2}} } \\ 0 \\ \end{array} \begin{array}{*{20}c} {t^{\tfrac{1} {2}} } \\ {wt^{\tfrac{1} {2}} } \\ \end{array} } \right):t \in F} \right\}. $$

(5.1)