Geometric Weil representations for star-analogues of SL(2,k)

Details Geometric Weil representations for star-analogues of SL(2,k) Geometric Weil representations for star-analogues of SL(2,k)

2010-06-27

arxiv.org/abs/1006.5236v1

Mathematics

Representation Theory

15 pages, submitted to Proceedings of the XVIII Latin American Algebra Colloquium (CLA XVIII)

Scientific paper

We present here an elementary geometric approach to the construction of Weil representations of the star-analogues $SL_\ast(2,A), A$ a ring or algebra with involution $\ast$, of the group SL(2, k), k a field, reminiscent of the quantum groups $SL_q(2,A)$. 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 representations obtained by both methods in the non - classical case of the finite truncated polynomial algebra $A_m$ of degree $m$ with its canonical involution and obtain the analogue of the Maslov Index in this case.

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