Restriction of Guichardet–Wigner pseudocharacters to subgroups
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Restriction of Guichardet–Wigner pseudocharacters to subgrouThe restrictions of Guichardet–Wigner pseudocharacters on Hermitian symmetric connected simply connected Lie groups to Lie subgroups are studied. The following question is discussed. Let G be a connected simply connected Hermitian symmetric Lie group, let H be a connected simply connected Hermitian symmetric Lie subgroup of G, and let KG be the preimage of a maximal compact subgroup K of the adjoint group G' of G. The pair (H;KH), where KH stands for the preimage in H of a maximal compact subgroup of the adjoint group of H, is said to be regular in (G;KG) if KH ⊂ KG. Let (H1;KH1 ) and (H2;KH2 ) be two regular pairs (for a given KG) of connected simply connected Hermitian symmetric Lie subgroups with isomorphic subgroups H1 and H2. Are the restrictions of the Guichardet–Wigner pseudocharacter on G to H1 and H2 also isomorphic? In this note, we answer the question in the negative.ps
Abstract
The restrictions of Guichardet–Wigner pseudocharacters on Hermitian symmetric connected simply connected Lie groups to Lie subgroups are studied. The following question is discussed. Let G be a connected simply connected Hermitian symmetric Lie group, let H be a connected simply connected Hermitian symmetric Lie subgroup of G, and let KG be the preimage of a maximal compact subgroup K of the adjoint group G0 of G. The pair (H;KH), where KH stands for the preimage in H of a maximal compact subgroup of the adjoint group of H, is said to be regular in (G;KG) if KH ⊂ KG. Let (H1;KH1 ) and (H2;KH2 ) be two regular pairs (for a given KG) of connected simply connected Hermitian symmetric Lie subgroups with isomorphic subgroups H1 and H2. Are the restrictions of the Guichardet–Wigner pseudocharacter on G to H1 and H2 also isomorphic? In this note, we answer the question in the negative.
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