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arXiv:1204.6235 [math.NT]AbstractReferencesReviewsResources

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

Terence Joseph Kivran-Swaine

Published 2012-04-27, updated 2013-03-23Version 3

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.

Comments: This paper has been withdrawn by the author due to an index error in the main theorem
Categories: math.NT, math.RT
Subjects: 11S15, 11T30, 22E35
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