Hyperbolic spaces,principal series,and $${\mathrm{O}}(2,\infty )$$O(2,∞) |
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Authors: | Pierre Py Arturo Snchez |
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Institution: | Pierre Py,Arturo Sánchez |
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Abstract: | We prove that there exists no irreducible representation of the identity component of the isometry group $${\mathrm{PO}}(1,n)$$ of the real hyperbolic space of dimension n into the group $${\mathrm{O}}(2,\infty )$$ if $$n\ge 3$$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of $${\mathrm{PO}}(1,n)^{\circ }$$ into the groups $${\mathrm{O}}(p,\infty )$$ for other values of p. |
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