%0 Generic %1 Garncarek2010 %A Łukasz Garncarek, %D 2010 %K analogs principal representation series thompsons %T Analogs of principal series representations for Thompson's groups $F$ and $T$ %U http://arxiv.org/abs/1008.1275 %X We define series of representations of the Thompson's groups $F$ and $T$, which are analogs of principal series representations of $SL(2,\R)$. We show that they are irreducible and classify them up to unitary equivalence. We also prove that they are different from representations induced from finite-dimensional representations of stabilizers of points under natural actions of $F$ and $T$ on the unit interval and the unit circle, respectively.

@misc{Garncarek2010, abstract = { We define series of representations of the Thompson's groups $F$ and $T$, which are analogs of principal series representations of $SL(2,\R)$. We show that they are irreducible and classify them up to unitary equivalence. We also prove that they are different from representations induced from finite-dimensional representations of stabilizers of points under natural actions of $F$ and $T$ on the unit interval and the unit circle, respectively. }, added-at = {2011-03-22T12:35:21.000+0100}, author = {Łukasz Garncarek}, biburl = {https://www.bibsonomy.org/bibtex/2f35016dd1e628bf4e364b2ca9afca57b/uludag}, description = {Analogs of principal series representations for Thompson's groups $F$ and $T$}, interhash = {d975115b43ddb3b55dfbb1e5a20e1972}, intrahash = {f35016dd1e628bf4e364b2ca9afca57b}, keywords = {analogs principal representation series thompsons}, note = {cite arxiv:1008.1275 Comment: (v1) 5 pages; (v2) 7 pages; a substantially rewritten version; improved presentation; some new material on induced representations; removed the "Another approach..." section}, timestamp = {2011-03-22T12:35:22.000+0100}, title = {Analogs of principal series representations for Thompson's groups $F$ and $T$}, url = {http://arxiv.org/abs/1008.1275}, year = 2010 }