On the wavefront sets associated with theta representations

Gao, Fan; Tsai, Wan-Yu

doi:10.1007/s00209-021-02894-5

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“…This invariant annihilator variety of an irreducible representation is closely related with many research fields, such as representations of Weyl groups, Kazhdan-Lusztig cells, and representations of Lie groups. See for example [BB82, BV82, BMSZa, BMSZb, BMSZc, GS13, GSK21, GT22,McG96]. But in general, even the annihilator variety of a highest weight module is not so easy to get for classical Lie algebras.…”

Section: Introductionmentioning

confidence: 99%

A characterization of the unitary highest weight modules by Euclidean Jordan algebras

Bai¹

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Let g be a classical Lie algebra. Let L(λ) be a highest weight module of g with highest weight λ − ρ, where ρ is half the sum of positive roots. In 1985, Joseph proved that the associated variety of a primitive ideal is the Zariski closure of a nilpotent orbit in g * . In this paper, we will give some combinatorial characterizations of the annihilator varieties of highest weight modules for classical Lie algebras. In fact, we will give two algorithms, i.e., bipartition algorithm and partition algorithm. Contents 1. Introduction 1.1. Bipartition algorithm 1.2. Partition algorithm 2. Annihilator varieties of highest weight modules 3. Representations of Weyl groups 3.1. B-symbol 3.2. D-symbol 3.3. Double cells and special symbols 4. The j-induction operator 4.1. Integral Weyl groups 4.2. The j-induction operator 5. The annihilator varieties for type A n−1 6. The annihilator varieties for types B n and C n 6.1. Bipartiton algorithm 6.2. Partition algorithm 7. The annihilator varieties for type D n 7.1. Lusztig-Spaltenstein induction 7.2. τ -invariant. 7.3. Bipartition algorithm 7.4. Partition algorithm 8. Hollow diagram algorithm 8.1. Hollow diagram 8.2. Hollow diagram and special Young diagram 8.3. Hollow diagram and the metaplectic special Young diagram Acknowledgments

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Section: Introductionmentioning

confidence: 99%

A characterization of the unitary highest weight modules by Euclidean Jordan algebras

Bai¹

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On the wavefront sets associated with theta representations

Cited by 1 publication

References 59 publications

A characterization of the unitary highest weight modules by Euclidean Jordan algebras

A characterization of the unitary highest weight modules by Euclidean Jordan algebras

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