Rational structures on quivers and a generalization of Gelfand's equivalence: Theorem B
For every field E of characteristic 0 and every integer l >= 0 (lambda = l^2), the category HC_lambda(sl_2, SO(2))_E of E-rational Harish-Chandra modules for (sl_2, SO(2)) with generalized infinitesimal character lambda is equivalent to the category Rep^nil(Gamma_E) of finite-dimensional nilpotent representations of an E-rational quiver Gamma_E: the Gelfand quiver (with the relation a_- b_- = a_+ b_+) if l >= 1 and the cyclic quiver if l = 0, carrying the action of Gal(E(sqrt(-1))/E) that swaps the two outer vertices when sqrt(-1) is not in E. For E = C this is Gelfand's classical…
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