The Clebsch-Gordan formulas for d-function are studied for both nonunitary finite dimensional representation and unitary infinite dimensional representation of the SU (1, 1) group. It is shown that, in addition to the usual Clebsch-Gordan formulas for the above-mentioned two representations, there exists an additional type of Clebsch-Gordan fornmla connecting the nonunitary and unitary d-functi...

We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2, R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2, R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into accoun...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act on M as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds...

E6 is an attractive group for unification model building. However, the complexity of a rank 6 group makes it non-trivial to write down the structure of higher dimensional operators in an E6 theory in terms of the states labeled by quantum numbers of the Standard Model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the 27...

A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, while the tracel...