The Minimal Unitary Representation of E_8(8)

We give a new construction of the minimal unitary representation of the exceptional group E_8(8) on a Hilbert space of complex functions in 29 variables. Due to their manifest covariance with respect to the E_7(7) subgroup of E_8(8) our formulas are simpler than previous realizations, and thus well suited for applications in superstring and M theory.Comment: 24 pages, 1 figure, version to be published in ATM

How polycentric is a monocentric city? The role of agglomeration economies

Can the demise of the monocentric economy across cities during the 20th century be explained by decreasing transport costs to the city center or are other fundamental forces at work? Taking a hybrid perspective of classical bid-rent theory and a world where clustering of economic activity is driven by (knowledge) spillovers, Berlin, Germany, from 1890 to 1936 serves as a case in point. We assess the extent to which firms in an environment of decreasing transport costs and industrial transformation face a trade-off between distance to the CBD and land rents and how agglomeration economies come into play in shaping their location decisions. Our results suggest that an observable flattening of the traditional distance to the CBD gradient may mask the emergence of significant agglomeration economies, especially within predominantly service-based inner city districts.Transport Innovations; Land Values; Location Productivity; Agglomeration Economies; Economic History; Berlin

How Polycentric is a Monocentric City? The Role of Agglomeration Economies

Can the demise of the monocentric economy across cities during the 20th century be explained by decreasing transport costs to the city center or are other fundamental forces at work? Taking a hybrid perspec¬tive of classical bid-rent theory and a world where clustering of economic activity is driven by (knowledge) spillovers, Berlin, Germany, from 1890 to 1936 serves as a case in point. We assess the extent to which firms in an environment of decreasing transport costs and industrial transformation face a trade-off between distance to the CBD and land rents and how agglomeration economies come into play in shaping their location deci¬sions. Our results suggest that an observable flattening of the traditional distance to the CBD gradient may mask the emergence of significant agglomeration economies, especially within predominantly service-based inner city districts.Transport Innovations, Land Values, Location Productivity, Agglomeration Economies, Economic History, Berlin.

On the generic finiteness of outcome distributions for bimatrix game forms

We provide an example of an outcome game form with two players for which there is in an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induce a continuum of outcome distributions. The case for three or more players has been settled by Govindan and McLennan [3]

On the generic finiteness of equilibrium outcome distributions in bimatrix game forms

We provide an example of an outcome game form with two players for which there is an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induces a continuum of outcome distributions.Publicad

Missing Modules, the Gnome Lie Algebra, and E10E_{10}

We study the embedding of Kac-Moody algebras into Borcherds (or generalized Kac-Moody) algebras which can be explicitly realized as Lie algebras of physical states of some completely compactified bosonic string. The extra ``missing states'' can be decomposed into irreducible highest or lowest weight ``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding lowest weights are associated with imaginary simple roots whose multiplicities can be simply understood in terms of certain polarization states of the associated string. We analyse in detail two examples where the momentum lattice of the string is given by the unique even unimodular Lorentzian lattice $II_{1,1}$ or $II_{9,1}$, respectively. The former leads to the Borcherds algebra $g_{1,1}$, which we call ``gnome Lie algebra", with maximal Kac-Moody subalgebra $A_1$. By the use of the denominator formula a complete set of imaginary simple roots can be exhibited, whereas the DDF construction provides an explicit Lie algebra basis in terms of purely longitudinal states of the compactified string in two dimensions. The second example is the Borcherds algebra $g_{9,1}$, whose maximal Kac-Moody subalgebra is the hyperbolic algebra $E_{10}$. The imaginary simple roots at level 1, which give rise to irreducible lowest weight modules for $E_{10}$, can be completely characterized; furthermore, our explicit analysis of two non-trivial level-2 root spaces leads us to conjecture that these are in fact the only imaginary simple roots for $g_{9,1}$.Comment: 31 pages, LaTeX2e, AMS packages, PSTRICK

Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.Comment: 36 page