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A group $G$ is generated by $g_1, 1, -1, g_1, g_2, \ldots, g_n$. The relation of its generators is given by a simple undirected graph $G = (V=[n], E)$, where $(i, j) \in E$ means $g_i g_j = -g_j g_i$. In the group $1$ is the identity such that $1g = g$ for any element $g$; $(-1)*(-1) = 1$, and $(-1)$ is commuting with all elements.

What are the unitary representations of such group?

I only know in the case $G = K_n$ (the complete graph), representation of this group is well studied in Clifford algebra.

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# Unitary representations of a group given generating set

A group $G$ is generated by $g_1, g_2, \ldots, g_n$. The relation of its generators is given by a simple undirected graph $G = (V=[n], E)$, where $(i, j) \in E$ means $g_i g_j = -g_j g_i$.

What are the unitary representations of such group?

I only know in the case $G = K_n$ (the complete graph), representation of this group is well studied in Clifford algebra.