Projection of Elliptic Orbits and Branching Laws

2024/01/26 by He, Hongyu
#22E #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2401.14984

Abstract

Let G be a Lie group, and H⊂ G a closed subgroup. Let π be an irreducible unitary representation of G. In this paper, we briefly discuss the orbit method and its application to the branching problem π|_H. We use the Gan-Gross-Prasad branching law for (G, H)= ( U(p,q), U(p, q-1) ) as an example to illustrate the relation between \pro_{\f u(p, q-1)}^{\f u(p,q)} \mc O(λ) and the branching law of the discrete series D_λ|_U(p,q-1) for λ an regular elliptic element. We also discuss some results regarding branching laws and wave front sets. The presentation of this paper does not follow the historical timeline of development.

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