  Let $H$ be a separable Hilbert space and $T$ be a self-adjoint bounded linear
operator on $H^{\otimes 2}$ with norm $\le1$, satisfying the Yang--Baxter
equation. Bo\.zejko and Speicher (1994) proved that the operator $T$ determines
a $T$-deformed Fock space $\mathcal F(H)=\bigoplus_{n=0}^\infty\mathcal
F_n(H)$. We start with reviewing and extending the known results about the
structure of the $n$-particle spaces $\mathcal F_n(H)$ and the commutation
relations satisfied by the corresponding creation and annihilation operators
acting on $\mathcal F(H)$. We then choose $H=L^2(X\to V)$, the $L^2$-space of
$V$-valued functions on $X$. Here $X:=\mathbb R^d$ and $V:=\mathbb C^m$ with
$m\ge2$. Furthermore, we assume that the operator $T$ acting on $H^{\otimes
2}=L^2(X^2\to V^{\otimes 2})$ is given by
$(Tf^{(2)})(x,y)=C_{x,y}f^{(2)}(y,x)$. Here, for a.a.\ $(x,y)\in X^2$,
$C_{x,y}$ is a linear operator on $V^{\otimes 2}$ with norm $\le1$ that
satisfies $C_{x,y}^*=C_{y,x}$ and the spectral quantum Yang--Baxter equation.
The corresponding creation and annihilation operators describe a multicomponent
quantum system. A special choice of the operator-valued function $C_{xy}$ in
the case $d=2$ determines non-Abelian anyons (also called plektons). For a
multicomponent system, we describe its $T$-deformed Fock space and the
available commutation relations satisfied by the corresponding creation and
annihilation operators. Finally, we consider several examples of multicomponent
quantum systems.
