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Dirac operator and its cohomology for the quantum group $U_q(\mathfrak{sl}_2)$ (1702.02435v2)
Published 8 Feb 2017 in math.RT, math-ph, math.FA, math.MP, and math.QA
Abstract: We introduce a Dirac operator $D$ for the quantum group $U_q(\mathfrak{sl}_2)$, as an element of the tensor product of $U_q(\mathfrak{sl}_2)$ with the Clifford algebra on two generators. We study the properties of $D$, including an analogue of Vogan's conjecture. We compute the cohomology of $D$ acting on various $U_q(\mathfrak{sl}_2)$-modules.