Thomas Bunke
IME-USP, Brazil
Construction of irreducible representations for SL2 over a finite field
Abstract: We construct the Weil representation and compute a realization for a model of Schrödinger representation over a vector space over a finite field (charF \ne 2). Embeddings of SL2 over the finite field into symplectic groups are classified employing quadratic forms of order n=1,2 and all irrep (upto iso) explicitely constructed by factoring the Sp modules by the actions of the corresponding ortogonal groups. The representations for characters of second order (S. Tanaka) can already be obtained by considering embeddings into in symplectic groups for n=1.