Dirac operator and its cohomology for the quantum group U_q(\mathfrak{sl}_2)

Authors: Pavle Pandžić, Petr Somberg

Journal of Mathematical Physics 58, 041702 (2017);


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.