Related papers: Generalized Kahler and hyper-Kahler quotients
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space G/K is generalized for each K-type in a certain class which we call `single-petaled'. The argument also includes a…
It is shown that Kazama-Suzuki conditions for the denominator subgroup of N=2 superconformal $G/H$ coset model determine Generalized K$\ddot{a}$hler geometry on the target space of the corresponding N=2 supersymmetric $\sigma$-model.
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\"ahler reduction; projective superspace; the generalized Legendre construction;…
We construct the entire generalized Kac-Moody Lie algebra as a quotient of the positive part of another generalized Kac-Moody Lie algebra. The positive part of a generalized Kac-Moody Lie algebra can be constructed from representations of…
We characterize the elements of generalized Gelfand Shilov spaces in terms of the coefficients of their Fourier-Hermite expansion. The technique we use can be applied both in quasianalytic and nonquasianalytic case. The characterizations…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras…
Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…
It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…
This paper reframes Riemannian geometry as a generalized Lie algebra allowing the equations of both RG and then General Relativity to be expressed as commutation relations among fundamental operators. We begin with an Abelian Lie algebra of…
We study the construction of generalized Kahler manifolds, described purely in terms of N=(2,2) semichiral superfields, by a quotient using the semichiral vector multiplet. Despite the presence of a b-field in these models, we show that the…
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…
In this paper, we first define the complexification of a real analytic map between real analytic Koszul manifolds and show that the complexified map is the holomorphic extension of the original map. Next we define an anti-Kaehler metric…
Due to its rich structure and close connection with gauge theory, hyperk\"ahler manifolds have attracted increasing interest. Using infinite dimensional hyperk\"ahler reduction, Kronheimer proved that certain adjoint orbits of complexified…