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Michael P. Tuite

  1. The Szeg\"o Kernel on a Sewn Riemann Surface.

    Втр, 02/23/2010 - 16:01 — SomNambul
    Authors: Michael P. Tuite, Alexander Zuevsky
    Subjects: Quantum Algebra
    Abstract

    We describe the Szeg\"o kernel on a higher genus Riemann surface in terms of
    Szeg\"o kernel data coming from lower genus surfaces via two explicit sewing
    procedures where either two Riemann surfaces are sewn together or a handle is
    sewn to a Riemann surface. We consider in detail the examples of the Szeg\"o
    kernel on a genus two Riemann surface formed by either sewing together two
    punctured tori or by sewing a twice-punctured torus to itself. We also consider
    the modular properties of the Szeg\"o kernel in these cases.

  2. Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I.

    Ср, 12/02/2009 - 16:01 — SomNambul
    Authors: Geoffrey Mason, Michael P. Tuite
    Subjects: Quantum Algebra
    Abstract

    We define the partition and $n$-point functions for a vertex operator algebra
    on a genus two Riemann surface formed by sewing two tori together. We obtain
    closed formulas for the genus two partition function for the Heisenberg free
    bosonic string and for any pair of simple Heisenberg modules. We prove that the
    partition function is holomorphic in the sewing parameters on a given suitable
    domain and describe its modular properties for the Heisenberg and lattice
    vertex operator algebras and a continuous orbifolding of the rank two fermion
    vertex operator super algebra.

  3. Vertex Operators and Modular Forms.

    Сб, 09/26/2009 - 04:10 — SomNambul
    Authors: Geoffrey Mason, Michael P. Tuite
    Subjects: Quantum Algebra
    Abstract

    The leitmotif of these Notes is the idea of a vertex operator algebra (VOA)
    and the relationship between VOAs and elliptic functions and modular forms.
    This is to some extent analogous to the relationship between a finite group and
    its irreducible characters; the algebraic structure determines a set of
    numerical invariants, and arithmetic properties of the invariants provides
    feedback in the form of restrictions on the algebraic structure. One of the
    main points of these Notes is to explain how this works, and to give some
    reasonably interesting examples.

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