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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)



    Chapter 1. Morphisms of canonical commutation relations and symplectic category

    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

    Chapter 2. Orthogonal category and morphisms of canonical anticommutation relations

    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 $GA$, $B$, $C$

    Chapter 3. Holomorphic extensions of representations of the group of diffeomorphisms of circle

    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 $Shtan$

    Chapter 4. Representations of the categories $GA$, $B$, $C$, $D$

    17. Classification theorem
    18. Construction of representations
    19. Proofs.

    Chapter 5. Representations of categories $U$, $Sp$, $SO*$

    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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