On Duflo's Theorem That Minimal Primitive Ideals Are Centrally Generated
✍ Scribed by Walter Borho
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 137 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let ᒄ be a complex semisimple Lie algebra. Duflo's theorem states that each Ž . minimal primitive ideal of the enveloping algebra U ᒄ is generated by its intersection with the center. We prove the following generalization. For the ''relative Ž . enveloping algebra'' A s U ᒄ rI relative to a parabolic subalgebra ᒎ of ᒄ, where Ž . I denotes the annihilator of the induced module U ᒄ m ,ރ let Z denote the UŽw ᒎ , ᒎ x. ˜˜c enter of A, let Z denote its normalization, and let A s AZ be the slight extension of A obtained by normalizing the center. We present a theorem that states that under certain conditions, which are always satisfied if ᒄ s ᒐ ᒉ , we have n that each minimal primitive ideal of A is generated by its intersection with the ˜Ž center Z. Duflo's theorem is the special case where ᒎ is a Borel subalgebra then ˜˜Ž ..