One-dimensional locally bounded not necessarily continuous pseudorepresentations of the group SL(2,Qp) with small defect are identity representations
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We prove that every one-dimensional not necessarily continuous locally bounded pseudorepresentation of the group SL(2;Qp) with sufficiently small defect is the ordinary identity representation of the group. Therefore, for every group generated by its subgroups isomorphic to SL(2;Qp), every onedimensional pseudorepresentation of the group with sufficiently small defect is the identity representation.
Abstract
We prove that every one-dimensional not necessarily continuous locally bounded pseudorepresentation of the group SL(2;Qp) with sufficiently small defect is the ordinary identity representation of the group. Therefore, for every group generated by its subgroups isomorphic to SL(2;Qp), every onedimensional pseudorepresentation of the group with sufficiently small defect is the identity representation.
참고문헌 (4)
- A. I. Shtern, "Finite-Dimensional Quasirepresentations of Connected Lie Groups and Mishchenko’s Conjecture", Fundam. Prikl. Mat, 13(7), pp.85~225 (2007)
- A. I. Shtern, "Finite-Dimensional Quasirepresentations of Connected Lie Groups and Mishchenko’s Conjecture", Fundam. J. Math. Sci. (N. Y. ), 159(5), pp.653~751 (2009)
- A. I. Shtern, "Specific properties of one-dimensional pseudorepresentations of groups", Fundam. Prikl. Mat, 21(1), pp.247~255 (2016)
- A. I. Shtern, "Specific properties of one-dimensional pseudorepresentations of groups", Fundam. in : J. Math. Sci. (N. Y. ), 233(5), pp.770~776 (2018)