Some irreducible free group representations in which a linear combination of the generators has an eigenvalue
2002 ◽
Vol 72
(2)
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pp. 257-286
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Keyword(s):
AbstractWe construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the eigenvalue is specified, we conjecture that there is only one such representation. The representation we have found is described explicitly (modulo inversion of a certain rational map on Euclidean space) in terms of a positive definite function, and also by means of a quasi-invariant probability measure on the combinatorial boundary of the group.
2006 ◽
Vol 09
(04)
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pp. 529-546
1969 ◽
Vol 21
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pp. 1309-1318
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1989 ◽
Vol 46
(3)
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pp. 415-422
2010 ◽
Vol 31
(5)
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pp. 1277-1286
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2018 ◽
Vol 61
(1)
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pp. 179-200