IJPAM: Volume 41, No. 4 (2007)

COMPUTING CASIMIR OPERATORS FOR
THE GENERALIZED UPPER HALF PLANE

Kevin A. Broughan
Department of Mathematics
University of Waikato
3105, Private Bag, Hamilton, NEW ZEALAND
e-mail: kab@waikato.ac.nz


Abstract.A program which computes the Casimir partial differential operators for the generalized upper half plane $\mathfrak{h}^n=GL(n,\mathbb{R})/O(n,\mathbb{R})\times \mathbb{R}^\times$ is described. The output from this program for small values of the dimension $n$ and order $m$ and eigenvalues for the operators acting on the ``power function" $I_\nu$ are also given. In dimension 3 the relationship between Bump's forms for the operators and the operators computed here is found to be $\Delta_1=\Delta_{2,3}/2,\Delta_2= \Delta_{3,3}/3-\Delta_{2,3}/2$ provided that a small amendment is made to the exponent of one factor in one term in Bump's operator.

Received: November 16, 2007

AMS Subject Classification: 32N10, 11F30, 11F55

Key Words and Phrases: computational algorithm, Casimir partial differential operators, Bump's forms,

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4