Relations among various versions of the Segal-Bargmann transform

Details Relations among various versions of the Segal-Bargmann transform Relations among various versions of the Segal-Bargmann transform

2009-12-13

arxiv.org/abs/0912.2547v1

Physics

Mathematical Physics

17 pages

Scientific paper

We present various relations among Versions A, B and C of the Segal-Bargmann transform. We get results for the Segal-Bargmann transform associated to a Coxeter group acting on a finite dimensional Euclidean space. Then analogous results are shown for the Segal-Bargmann transform of a connected, compact Lie group for all except one of the identities established in the Coxeter case. A counterexample is given to show that the remaining identity from the Coxeter case does not have an analogous identity for the Lie group case. A major result is that in both contexts the Segal-Bargmann transform for Version C is determined by that for Version A.

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