Casimir energy inside a triangle

For certain class of triangles (with angles proportional to \fr{\pi}{N}, $N\geq 3$) we formulate image method by making use of the group $G_N$ generated by reflections with respect to the three lines which form the triangle under consideration. We formulate the renormalization procedure by classification of subgroups of $G_N$ and corresponding fixed points in the triangle. We also calculate Casimir energy for such geometries, for scalar massless fields. More detailed calculation is given for odd $N$.Comment: Latex, 13 page

Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra

SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived.Comment: Latex, 8 page

Two Dimensional Fractional Supersymmetry from the Quantum Poincare Group at Roots of Unity

A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the pseudo-unitary, irreducible representations of them are obtained. The matrix elements of these representations are explicitly constructed.Comment: 10 pages. Some misprints are corrected. To appear in J. Phys.