Geometric Weil representations for star-analogues of SL(2,k)
We present here an elementary geometric approach to the con- struction of Weil representations of the star-analogues SL�(2,A), A a ring or algebra with involution �, of the group SL(2, k), k a field, reminiscent of the quantum groups SLq(2,A). We review as well the elementary construction of Weil representations for these groups via generators and relations, which uses the Bruhat presentation available in many cases. We compare the repre- sentations obtained by both methods in the non - classical case of the finite truncated polynomial algebra Am of degree m with its canonical involution and obtain the analogue of the Maslov Index in this case.