A functional approach to a Gelfand-Tsetlin type base for ${\mathfrak{o}}_5$

Abstract

A realization of representations of the Lie algebra ${\mathfrak{o}}_5$ in the space of functions on a group $Spi{n}_5\simeq S{p}_4$ is considered. In a representation we take a Gelfand-Tsetlin type base associated with a restriction ${\mathfrak{o}}_5\downarrow {\mathfrak{o}}_3$. Such a base is useful is problems appearing in quantum mechanics. We construct explicitely functions on the group that correspond to base vectors. As in the cases of Lie algebras ${\mathfrak{gl}}_3$, ${\mathfrak{sp}}_4$ these functions can be expressed through $A$-hypergeometric functions (this does not hold for algebras of these series in higher dimentions). Using this realization formulas for the action of generators are obtained.

24 pages

References in corpus (1)

• Noncommutative pfaffians and classification of states of five-dimensional quasi-spin