SL(2,Qp), p ≠ 2, has no nontrivial continuous finite-dimensional pseudorepresentations
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As is well known, the group SL(2,Qp) has no nontrivial continuous finite-dimen-sional representations. It is proved that this group has no nontrivial continuous finite-dimensional pseudorepresentations either. This supports the conjecture that the simple Chevalley groups over totally disconnected locally compact fields of characteristic zero have no nontrivial continuous finite-dimensional pseudorepresentations.
Abstract
As is well known, the group SL(2,Qp) has no nontrivial continuous finite-dimen-sional representations. It is proved that this group has no nontrivial continuous finite-dimensional pseudorepresentations either. This supports the conjecture that the simple Chevalley groups over totally disconnected locally compact fields of characteristic zero have no nontrivial continuous finite-dimensional pseudorepresentations.
참고문헌 (6)
- I. M. Gelfand, "Representations of a group of matrices of the second order with elements from a locally compact eld, and special functions on locally compact fields", Uspekhi Mat. Nauk, 18(4), pp.29~99 (1963)
- A. I. Shtern, "Quasisymmetry. I", Russ. J. Math. Phys, 2(3), pp.353~382 (1994)
- A. I. Shtern, "Triviality and Continuity of Pseudocharacters and Pseudorepresentations", Russ. J. Math. Phys, 5(1), pp.135~138 (1998)
- A. I. Shtern, "Bounded Continuous Real 2-Cocycles on Simply Connected Simple Lie Groups and Their Applications", Russ. J. Math. Phys, 8(1), pp.122~133 (2001)
- A. I. Shtern, "Quasisymmetry. II", Russ. J. Math. Phys, 14(3), pp.332~346 (2007)
- J. E. Humphreys, "Linear Algebraic Groups, Graduate Texts in Mathematics" (1975), Springer- Verlag