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On generalized Weil representations over involutive rings

2011; American Mathematical Society; Linguagem: Inglês

10.1090/conm/544/10751

1098-3627

Luis García Gutiérrez, José Pantoja, Jorge Soto‐Andrade,

Algebraic structures and combinatorial models

We construct via generators and relations, generalized Weil representations for analogues of classical SL(2, k), k a field, over involutive base rings (A, * ).This family of groups covers different kinds of groups, classical and non classical.We give some examples that include symplectic groups as well as non classical groups like SL * (2, Am), where Am is the finite modular analogue of the algebra of real m-jets in one dimension with its canonical involutive symmetry.