The star exponential and path integrals on compact groups. II: The Weyl character formula (Q1317885)

Let \(G\) be a compact simply connected Lie group and let \(H \subset G\) be a maximal torus. By using Borel-Weil-Bott construction of a holomorphic line bundle and the space of holomorphic sections with a metric, the associated unitary irreducible representation and the dequantization procedure of Berezin, the author in collaboration with \textit{A. C. Cadavid} [part I of this paper, ibid. 23, No. 2, 111-115 (1991; Zbl 0747.58019)] defined a \(G\)-invariant star product. In the present work an expression for the Weyl character formula is obtained in terms of the star product path integral. The relationship between path integrals constructed with the star product and with coadjoint orbits is also studied.