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arXiv · 1204.6235

Stabilizers of simple paths in the Bruhat-Tits tree of SL(2) over finite extensions of Q2

Terence Joseph Kivran-Swaine
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Abstract

For F an algebraic extension of Q2, the conjugacy classes of invertible, 2-by-2, trace-zero matrices under the action of G := SL2(F) are analyzed relative to the quadratic extension that splits the respective characteristic polynomial. The stabilizer in G of each such matrix is computed as a stabilizer of a simple, Galois invariant path in the Bruhat-Tits Tree of G.

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Terence Joseph Kivran-Swaine. 2013-03-23. Stabilizers of simple paths in the Bruhat-Tits tree of SL(2) over finite extensions of Q2. https://arxiv.org/abs/1204.6235

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