  This article constructs the Hilbert space for the algebra $\alpha \beta -
e^{i \theta} \beta \alpha = 1 $ that provides a continuous interpolation
between the Clifford and Heisenberg algebras. This particular form is inspired
by the properties of anyons. We study the eigenvalues of a generalized number
operator (${\cal N} = \beta \alpha$) and construct the Hilbert space,
classified by values of a complex coordinate ($\lambda_0$): the eigenvalues lie
on a circle. For $\theta$ being an irrational multiple of $2 \pi$, we get an
infinite-dimensional representation, however for a rational multiple
($\frac{M}{N}$) of $2 \pi$, it is finite-dimensional, parametrized by the
complex coordinate $\lambda_0$. The case for $N=2 \: ; \: \theta=\pi$ is the
usual Clifford algebra for fermions, while the case for $N=\infty \: ; \:
\theta=0$ is the Heisenberg algebra of bosons, albeit with two copies for
positive and negative eigenvalues. We find a smooth transition from the fermion
to the boson situation as $N \rightarrow \infty$ from $N=2$. After constructing
the Hilbert space from the algebra, the cases for $N=2,3$ can be mapped to
$SU(2)$. Then, we motivate the study of coherent states, rather generally. The
coherent states are eigenstates of $\alpha$, the annihilation operator and are
labeled by complex numbers for non-zero $\lambda_0$.
