Related papers: Analogs of principal series representations for Th…

We prove irreducibility and mutual inequivalence for certain unitary representations of R. Thompson's groups F and T.

Jones introduced unitary representations for the Thompson groups $F$ and $T$ from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups $\vec{F}$ and…

M. Hanzer and I. Matic have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal…

We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson groups called Pythagorean. For each natural number d we…

In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations"…

For p odd, the Lie group SO_0(p+1,p+1) has a family of unitary degenerate principal series representations realized on the space of real (p+1) by (p+1) skew symmetric matrices, similar to the Stein's complementary series for SL(2n,C) or…

Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations of the Thompson's group $F$ equipped with canonical (vacuum)…

In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

The Thompson group F has a natural unitary representation on $H=L^2[0,1]$. With some projections, we construct a family of projective unitary representations on a Fermionic Fock space associated with $H$. It comes from the representation of…

The work of Bernstein-Zelevinsky and Zelevinsky gives a good understanding of irreducible subquotients of a reducible principal series representation of $GL_n(F)$, $F$ a $p$-adic field (without specifying their multiplicities which is done…

In this paper, we introduce a study of prolongations of representations of Lie groups. We obtain a faithful (one-to-one) representation of TG where G is a finite-dimensional Lie group and TG is the tangent bundle of G, by using (not…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…

In a previous paper, we defined a higher dimensional analog of Thompson's group V, and proved that it is simple, infinite, finitely generated, and not isomorphic to any of the known Thompson groups. There are other Thompson groups that are…

We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a…

We prove that the only finite factor-representations of the Higman-Thompson groups $\{F_{n,r}\}$, $ \{G_{n,r}\}$ are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that…