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Journal of Lie Theory 30 (2020), No. 3, 705--714
Copyright Heldermann Verlag 2020

Kobayashi's Conjecture on Associated Varieties for Klein Four Symmetric Pairs (E6(-14), Spin(8,1))

Haian He
Dept. of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

We confirm a conjecture on associated varieties by Toshiyuki Kobayashi for the Klein four symmetric pair (E6(-14), Spin(8,1)), which provides an alternative way to confirm the conjecture for the symmetric pair (Spin(8,2), Spin(8,1)). Also, for Klein four symmetric pairs (G, GΓ) with the exceptional simple Lie groups G of Hermitian type, there exists a discrete series representation of G which is GΓ-admissible if and only if (G, GΓ) is of holomorphic type.

Keywords: Associated variety, discrete branching law, discrete series representation, Klein four symmetric pair.

MSC: 22E46, 22E47.

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