Strict quantization of coadjoint orbits

TY - JOUR

T1 - Strict quantization of coadjoint orbits

AU - Schmitt, Philipp

N1 - 45 pages. Comments are welcome!

PY - 2019/7/6

Y1 - 2019/7/6

N2 - We obtain a strict quantization of the holomorphic functions on any semisimple coadjoint orbit of a complex semisimple connected Lie group. By restricting this quantization, we also obtain strict star products on a subalgebra of analytic functions for any semisimple coadjoint orbit of a real semisimple connected Lie group. If this Lie group was also compact, the star product is of Wick type. The main tool to construct our quantization is a construction by Alekseev--Lachowska and an explicit formula for the canonical element of the Shapovalov pairing between generalized Verma modules.

AB - We obtain a strict quantization of the holomorphic functions on any semisimple coadjoint orbit of a complex semisimple connected Lie group. By restricting this quantization, we also obtain strict star products on a subalgebra of analytic functions for any semisimple coadjoint orbit of a real semisimple connected Lie group. If this Lie group was also compact, the star product is of Wick type. The main tool to construct our quantization is a construction by Alekseev--Lachowska and an explicit formula for the canonical element of the Shapovalov pairing between generalized Verma modules.

KW - math.QA

M3 - Journal article

VL - arXiv:1907.03185

JO - arXiv.org

JF - arXiv.org

ER -