Spinors are special representations of $\operatorname{Spin}(n)$ group which is double cover of $\operatorname{SO}(n)$. I am familiar with tetrad formalism and spin connection. $\operatorname{GL}(n,R)$ is not isomorphic to $\operatorname{Spin}(n)$. In GR literatures, it is usually said that $\operatorname{GL}(n,R)$ has not spinor representation. I don't understand what spinor representation of $\operatorname{GL}(n,R)$ is. Can someone explain what it mean when we say $\operatorname{GL}(n,R)$ has not spinor representation.
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