p-adic Banach space representations of SL₂(ℚ_p)

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发表日期：

2025年2月3日

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Dubravka Ban,
Matthias Strauch

摘要

We consider the restriction to SL₂(ℚ_p) of an irreducible p-adic unitary Banach space representation Π of GL₂(ℚ_p). If Π is associated, via the p-adic local Langlands correspondence, to an absolutely irreducible 2-dimensional Galois representation ψ, then the restriction of Π decomposes as a direct sum of r ≤ 2 irreducible representations. The main result of this paper is that r is equal to the cardinality s of the centralizer in PGL₂ of the projective Galois representation $\overline{\psi}$ $\bar{ψ}$ associated to ψ, and the restriction is multiplicity-free, except if ψ is triply-imprimitive, in which case s = 4 and the restriction of Π is a direct sum of two equivalent representations.

p-adic Banach space representations of SL2(ℚp)

摘要

p-adic Banach space representations of SL₂(ℚ_p)