  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.
