On the Representation Theory of Negative Spin

Details On the Representation Theory of Negative Spin On the Representation Theory of Negative Spin

2002-07-12

arxiv.org/abs/hep-th/0207121v1

Nucl.Phys. B645 (2002) 387-402

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, no figures, Latex2e

Scientific paper

10.1016/S0550-3213(02)00635-1

We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive and negative representations with the help of generalized characters and write down explicit reduction formulae for the products. From the characters, we define effective dimensions for the negative spin representations, find that they are fractional, and point out that the dimensions behave consistently under multiplication and decomposition of representations.

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