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Neretin Yury Aleksandrovich
Categories enveloping infinite dimensional groups and
representations of the category of Riemann surfaces
Doctoral degree thesis, Moscow Institute of Electronic Engineering, 1990
(Russian)
1. Gaussian operators $B[S]$.
2. Symplectic category and Weil representation
3. Symplectic category and symmetric spaces
4. Boundedness theorem for Gaussian operators
5. Affine symplectic category
6. Berezin operators in fermion Fock space
7.Boundedness of Berezin operators in polynormed fermion Fock space
8. Orthogonal category and spinor representation
9. Berezin operators in Hilbert space
10. Categories $GA$, $B$, $C$
11. Virasoro algebra
12. Semigroup $\Gamma$
13. Constructions of representations of the semigroup $\Gamma$
14. Explicit formulae
15. Category §Shtan$
16. Representations of the category $Shtan$
17. Classification theorem
18. Construction of representations
19. Proofs.
20. Categories $U$, $Sp$, $SO*$ and Howe duality
21. Proof of duality.
22. Generalized fractional linear maps as morphisms
of symmetric spaces
23. Categories enveloping infinite dimensional groups
Doctoral Degree in 1992 from MIAN (Steklov Mathematical Institute, RAN, Moscow)
Phys.-Math.Sciences; 01.01.06
Referees: A.N.Rudakov, A.L.Onishchik, R.I.Grigorchuk
Superwising Institute: POMI (St.-Petersburg Branch of Steklov Mathematical Institute RAN, St.-Petersburg)
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