Poisson sigma model and semiclassical quantization of integrable systems

In this paper we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The semiclassical path integral is defined as a formal power series with coefficients being Feynman diagrams. We also argue that in a similar way one can obtain irreducible semiclassical representations of Kontsevich's star product.Comment: 22 pages, 12 figure

On C*-algebras associated to right LCM semigroups

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroups or semigroups that satisfy Clifford's condition. Our main findings are results about uniqueness of the full semigroup C*-algebra. We build our analysis upon a rich interaction between the group of units of the semigroup and the family of constructible right ideals. As an application we identify algebraic conditions on S under which C*(S) is purely infinite and simple.Comment: 31 page

C*-Algebras of algebraic dynamical systems and right LCM semigroups

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As part of our analysis of these C*-algebras we prove results for right LCM semigroups. More precisely we discuss functoriality of the full semigroup C*-algebra and compute its K-theory for a large class of semigroups. We introduce the notion of a Nica-Toeplitz algebra of a product system over a right LCM semigroup, and show that it provides a useful alternative to study algebraic dynamical systems.Comment: 28 pages, to appear in Indiana Univ. Math.

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

Equilibrium states on right LCM semigroup C*-algebras

We determine the structure of equilibrium states for a natural dynamics on the boundary quotient diagram of $C^*$-algebras for a large class of right LCM semigroups. The approach is based on abstract properties of the semigroup and covers the previous case studies on $\mathbb{N} \rtimes \mathbb{N}^\times$, dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the same time, it provides new results for large classes of right LCM semigroups, including those associated to algebraic dynamical systems.Comment: 43 pages, to appear in Int. Math. Res. No

Monodromy Matrix in the PP-Wave Limit

We construct the monodromy matrix for a class of gauged WZWN models in the plane wave limit and discuss various properties of such systems.Comment: 16 page

Arbitrary Spin Representations in de Sitter from dS/CFT with Applications to dS Supergravity

We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to Euclidean conformal ones at one dimension lower. These results are then used to revisit an old question: can a consistent de Sitter supergravity be constructed, at least within its intrinsic horizon?Comment: 19 pages LaTex, references added, version to appear Nucl. Phys.