67 research outputs found

    Yangian Construction of the Virasoro Algebra

    Full text link
    We show that a Yangian construction based on the algebra of an infinite number of harmonic oscillators (i.e. a vibrating string) terminates after one step, yielding the Virasoro algebra.Comment: 5 pages, AMS-Latex 2

    Search-Money-and-Barter Models of Financial Stabilization

    Full text link
    A macroeconomic model based on search-theoretical foundations is built to show that in an economy with structural deficiencies of the Russian Virtual Economy, money substitutes appear as a result of optimizing behavior of agents. Moreover, the volume of money substitutes is typically large, and it is impossible to reduce their volume significantly by using standard instruments as an increase of the money supply or decreasing the tax level. The result obtains for an economy, where there are large natural monopolies and widespread informal networks.http://deepblue.lib.umich.edu/bitstream/2027.42/39716/3/wp332.pd

    Intertwining operators and Hirota bilinear equations

    Full text link
    An interpretation of Hirota bilinear relations for classical τ\tau functions is given in terms of intertwining operators. Noncommutative example of Uq(sl2)U_q(sl_2) is presented.Comment: Latex, 13 pages, no figures. Contribution to the Proceedings of Alushta Conference, June 199

    Optimal Stopping in Levy Models, for Non-Monotone Discontinuous Payoffs

    Get PDF
    We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit

    Meromorphic tensor equivalence for Yangians and quantum loop algebras

    Get PDF
    Let g{\mathfrak g} be a complex semisimple Lie algebra, and Yh(g)Y_h({\mathfrak g}), Uq(Lg)U_q(L{\mathfrak g}) the corresponding Yangian and quantum loop algebra, with deformation parameters related by q=exp⁥(πih)q=\exp(\pi i h). When hh is not a rational number, we constructed in arXiv:1310.7318 a faithful functor Γ\Gamma from the category of finite-dimensional representations of Yh(g)Y_h ({\mathfrak g}) to those of Uq(Lg)U_q(L{\mathfrak g}). The functor Γ\Gamma is governed by the additive difference equations defined by the commuting fields of the Yangian, and restricts to an equivalence on a subcategory of Yh(g)Y_h({\mathfrak g}) defined by choosing a branch of the logarithm. In this paper, we construct a tensor structure on Γ\Gamma and show that, if ∣q∣≠1|q|\neq 1, it yields an equivalence of meromorphic braided tensor categories, when Yh(g)Y_h({\mathfrak g}) and Uq(Lg)U_q(L{\mathfrak g}) are endowed with the deformed Drinfeld coproducts and the commutative part of the universal RR-matrix. This proves in particular the Kohno-Drinfeld theorem for the abelian qqKZ equations defined by Yh(g)Y_h({\mathfrak g}). The tensor structure arises from the abelian qqKZ equations defined by a appropriate regularisation of the commutative RR-matrix of Yh(g)Y_h({\mathfrak g}).Comment: Title changed, details added. 67 pages, 1 figure. Final version, to appear in Publ. Math IHE

    A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

    Full text link
    In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, S≄ΔIHS\geq \varepsilon I_{\mathcal{H}} for some Δ>0\varepsilon >0 in a Hilbert space H\mathcal{H} to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for HK,ΩH_{K,\Omega}, the Krein--von Neumann extension of the perturbed Laplacian −Δ+V-\Delta+V (in short, the perturbed Krein Laplacian) defined on C0∞(Ω)C^\infty_0(\Omega), where VV is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn\Omega\subset\mathbb{R}^n belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,rC^{1,r}, r>1/2r>1/2.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

    Pricing of perpetual Bermudan options

    No full text
    We consider perpetual Bermudan options and more general perpetual American options in discrete time. For wide classes of processes and pay-offs, we obtain exact analytical pricing formulae in terms of the factors in the Wiener-Hopf factorization formulae. Under additional conditions on the process, we derive simpler approximate formulae.

    On PBW bases for Yangians

    No full text

    Feller processes of normal inverse Gaussian type

    No full text
    We consider the construction of normal inverse Gaussian (NIG) (and some related) Levy processes from the probabilistic viewpoint and from that of the theory of pseudo-differential operators; we then introduce and analyse natural generalizations of these constructions. The resulting Feller processes are somewhat similar to the NIG Levy process but may, for instance, possess mean-reverting features. Possible applications to financial mathematics are discussed, and approximations to solutions of corresponding generalizations of the Black-Scholes equation are derived.

    On Fock space representations of quantized enveloping algebras related to non-commutative differential geometry

    No full text
    In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding q-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the q-deformed flag manifold
    • 

    corecore