A unitary 'quantization commutes with reduction' map for the adjoint action of a compact Lie group. (12th June 2018)

• Record Type: Journal Article
• Authors: Hall, Brian C; Lewis, Benjamin D
• Is Part Of: Quarterly journal of mathematics. Volume 69:Part 4(2018)
• Page Start: 1387
• Page End: 1421
• Publication Date: 2018-06-12
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/hay029
• Languages: English
• ISSNs: 0033-5606

Abstract

Abstract: Let K be a simply connected compact Lie group and T * ( K ) its cotangent bundle. We consider the problem of 'quantization commutes with reduction' for the adjoint action of K on T * ( K ) . We quantize both T * ( K ) and the reduced phase space using geometric quantization with half-forms. We then construct a geometrically natural map from the space of invariant elements in the quantization of T * ( K ) to the quantization of the reduced phase space. We show that this map is a constant multiple of a unitary map.