Affinoid enveloping algebras and their representations
<p>We develop the basic theory of Picard algebroids and twisted differential operators on a smooth, reduced, locally of finite type scheme over a commutative ring. We also give a new geometric proof of the classical Duflo's theorem. We next move to the study the affinoid enveloping alg...
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| Format: | Thesis |
| Language: | English |
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2020
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| Summary: | <p>We develop the basic theory of Picard algebroids and twisted differential operators on a smooth, reduced, locally of finite type scheme over a commutative ring. We also give a new geometric proof of the classical Duflo's theorem.
We next move to the study the affinoid enveloping algebra of a semisimple Lie algebra defined over a discrete valuation ring. We prove that there exists a one-to-one correspondence between the lattice of submodules of an affinoid Verma module of a given weight and the corresponding classical Verma module. Finally, we classify all the primitive ideals in the affinoid enveloping algebra and prove that a large class of two-sided ideals in the affinoid enveloping algebra is controlled by two-sided ideals in the classical enveloping algebra.</p>
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