Representation theoretic embedding of twisted Dirac operators

2021/02/06 by Mehdi, Salah, Pandzic, Pavle
#22E46 #43A85 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2102.03562

Abstract

Let G be a non-compact connected semisimple real Lie group with finite center. Suppose L is a non-compact connected closed subgroup of G acting transitively on a symmetric space G/H such that L∩ H is compact. We study the action on L/L∩ H of a Dirac operator D_G/H(E) acting on sections of an E-twist of the spin bundle over G/H. As a byproduct, in the case of (G,H,L)=(SL(2,\mathbb R)× SL(2,\mathbb R),Δ(SL(2,\mathbb R)× SL(2,\mathbb R)),SL(2,\mathbb R)× SO(2)), we identify certain representations of L which lie in the kernel of D_G/H(E).

Related

• The Dirac operator on compact symmetric spaces
• Harmonic spinors on homogeneous spaces
• Dirac operators twisted by ramified Euclidean line bundles
• Quantization of Hamiltonian loop group spaces
• The equivariant index of twisted dirac operators and semi-classical limits