Classification of Klein four symmetric pairs of holomorphic type for $$\mathrm {E}_{7(-25)}$$ E 7 ( - 25 )

Let [Formula: see text] be a Klein four symmetric pair. The author wants to classify all the Klein four symmetric pairs [Formula: see text] such that there exists at least one nontrivial unitarizable simple [Formula: see text]-module [Formula: see text] that is discretely decomposable as a [Formula: see text]-module. In this paper, three assumptions will be made. First, [Formula: see text] is an exceptional Lie group of Hermitian type, i.e. [Formula: see text] or [Formula: see text]. Second, [Formula: see text] is noncompact. Third, there exists an element [Formula: see text] corresponding to a symmetric pair of anti-holomorphic type such that [Formula: see text] is discretely decomposable as a [Formula: see text]-module.

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Classification of Klein four symmetric pairs of holomorphic type for $$\mathrm {E}_{7(-25)}$$ E 7 ( - 25 )

Cited by 6 publications

References 10 publications

Discrete decomposability of restrictions of $$({\mathfrak {g}},K)$$-modules for $$(G,G^\sigma )$$ with an automorphism $$\sigma $$ of even order

Discrete decomposability of restrictions of $$({\mathfrak {g}},K)$$-modules for $$(G,G^\sigma )$$ with an automorphism $$\sigma $$ of even order

Branching laws of Klein four-symmetric pairs for $$\textrm{Sp}(n,\mathbb {R})$$

Discretely decomposable restrictions of (𝔤,K)-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian type

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