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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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