{"id":"palomar/PALOMAR-2026-11-01-000018","url":"https://github.com/drjanosch42/rational_quivers/tree/414ccfd961f476a878c2d2aa1e54b42a50210de3/palomar","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-01-000018-v1.json","repo":"https://github.com/drjanosch42/rational_quivers","tags":["math.RT","math.RA","msc:16G20","msc:22E47","msc:68V20"],"score":0,"title":"Rational structures on quivers and a generalization of Gelfand's equivalence: Theorem B","trust":"high","domain":"math.RT","source":"palomar","authors":["Fabian Januszewski"],"reviews":0,"subject":"math.RT","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-01","reactions":{},"formalized":true,"formalizes":[{"title":"Rational structures on quivers and a generalization of Gelfand's equivalence","identifier":"arXiv:2506.23251","relationship":"formalizes"}]}