Unitary representations of the universal cover of SU(1,1) and tensor products

Parabolically induced unitary representations of the universal group U(F)^+ are C_0

By employing a new strategy we prove that all parabolically induced unitary representations of the Burger-Mozes universal group U(F)^+, with F being primitive, have all their matrix coefficients vanishing at infinity. This generalizes the same well-known result for the universal group U(F)^+, when F is 2-transitive.

Zero patterns and unitary similarity

A subspace of the space, L(n), of traceless complex $n\times n$ matrices can be specified by requiring that the entries at some positions $(i,j)$ be zero. The set, $I$, of these positions is a (zero) pattern and the corresponding subspace of L(n) is denoted by $L_I(n)$. A pattern $I$ is universal if every matrix in L(n) is unitarily similar to some matrix in $L_I(n)$. The problem of describing the universal patterns is raised, solved in full for $n\le3$, and partial results obtained for $n=4$. Two infinite families of universal patterns are constructed. They give two analogues of Schur's trian…

Galois and universal universal coverings of linear categories and fibre products

Let $k$ be a commutative ring. We study the behaviour of coverings of $k$-categories through fibre products and find a criterion for a covering to be Galois or universal.

例外情形下酉最高权模的分类

On the classification of unitary highest weight modules in the exceptional cases

本文利用Dirac不等式和PRV积，完成了例外李群$SO_e(2,n)$、$E_{6(-14)}$和$E_{7(-25)}$的万有覆盖的酉最高权模分类，并描述了给定无穷小特征的此类模。

Positive definite superfunctions and unitary representations of Lie supergroups

For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear functionals on the corresponding universal enveloping algebra which correspond to matrix coefficients of analytic unitary representations.

Free unitary groups are (almost) simple

We show that the quotients of Wang and Van Daele's universal quantum groups by their centers are simple in the sense that they have no normal quantum subgroups, thus providing the first examples of simple compact quantum groups with non-commutative fusion rings.