Tags:
Mathematics,
Classification of Lie algebras,
Harmonic analysis on Lie groups,
Operator algebras
Publications

Sund, Terje & Pavel, Liliana (2002). Monoid extensions admitting cocycles. Semigroup Forum.
ISSN 00371912.
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We characterize those monoid extensions which are associated to a certain class of 2cocycles. Algebraic, topological as well as involutive aspects are discussed. Applications to representation theory are given.
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Sund, Terje (2001). Monotony of certain free group representations. Mathematical Reviews.
ISSN 00255629.
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Let $\Gamma$ be a free nonabelian group on finitely many generators. Fix a basis for $\Gamma$ and let $A$ consist of the basis elements and their inverses. The Cayley graph $\frak T$ of $\Gamma$ with respect to $A$ has $\Gamma$ as its vertex set and has an edge between each pair of vertices $\{ x, xa \},\ x\in \Gamma, a\in A.$ $\frak T$ is a homogenous tree. The boundary $\Omega$ of $\frak T$ may be identified with the space of all infinite reduced words of letters from $A$. $\Gamma\cup\Omega$ is endowed with a certain subspace topology which makes $\Omega$ compact. A boundary representation $\pi$ of $\Gamma$ is constructed from a pair $(\nu, P(x,\omega))$ where $(i)$ $\nu$ is a Radon measure on $\Omega$ and $d\nu(x^{1}\omega)$ is absolutely continuous with respect to $d\nu(\omega),\ x\in\Gamma.$ $(ii)$ $P$ maps $\Gamma\times\Omega$ into $\Bbb C$ and $P(x,\omega)$ is $\nu$measurable in $\omega$. $(iii)$ P(x,\omega)^2=d\nu(x^{1}\omega)/d\nu(\omega) $(iv)$ $P(xy,\omega)=P(x,\omega)P(u,x^{1}\omega)$ $\pi$ acts on $L^2(\Omega,d\nu)$ and is defined by $$(\pi(x)F)(\omega)=P(x,\omega)F(x^{1}\omega)$$ The analogous construction for semisimple Lie groups is induction from a character of a parabolic subgroup. Many representations $\pi$ (such as the anisotropic principal series) in the reduced unitary dual $hat{\Gamma}_{red}$ of $\Gamma$ may be realized as boundary representations in two essentially different ways. In an earlier paper, the authors associated to certain functions $h: A\to\Bbb C$ a unitary representation $\pi_h$ of $\Gamma$ on $L^2(\Omega, d\vu_h)$ for a certain probability measure $\nu_h$, [M. G. Kuhn and T. Steger. More irreducible boundary representations of free groups, Duke Math. J., 82 (1996), 381436] In the paper under review, they show that $\pi_h$ does not have any other boundary realizations and, in addition, they provide a new proof that $\pi_h$ is irreducible.

Sund, Terje (2000, 01. desember). Om usikkerheten i slektstrær (Alle har en gal tiptiptipoldefar). [Radio].
Oslo.

Sund, Terje (2000). Squareintegrable imprimitivity systems. Mathematical Reviews.
ISSN 00255629.

Sund, Terje (1999). Generalization of the Mackey induction procedure, by L. Pavel. Mathematical Reviews.
ISSN 00255629.

Sund, Terje (1999). Groups with bounded trace.
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It will be shown that a connected Lie group has bounded trace if and only if its component with no semisimple factors has a cocompact radical which is a direct product $E\times R$ where $E$ denotes a finite direct product of groups of motion of the real plane (including covering groups) and $R$ is a semidirect product of a torus and a nilpotent group with continuous trace.

Sund, Terje (1999). Groups with trivial cortex.
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We give a complete description of the class of all connected Lie groups whose identity representation constitutes a separated point in the unitary dual.

Sund, Terje (1999). On nonunitary induced representations, by K. Kumahara. Mathematical Reviews.
ISSN 00255629.
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Published Nov. 30, 2010 11:20 PM
 Last modified Oct. 31, 2011 2:50 PM