Dirac operator and its cohomology for the quantum group Uq(sl(2))

Abstract

We introduce a Dirac operator D for the quantum group U-q(sl(2)), as an element of the tensor product of U-q(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(sl(2))-modules.

Keywords

• Dirac operator
• Quantum groups
• Vogan's conjecture