Robert P. Boyer

Character theory of infinite wreath products

The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” The K0-invariant of the group C∗-algebra is also determined.

Characters of the infinite symplectic group—A Riesz ring approach☆

We classify both the finite and infinite characters of the inductive limit symplectic group G. An important feature of our technique is the systematic use of a multiplicative structure on an “ordered completion” of the K0-group for the group C∗-algebra A of G. We also give explicit examples of the K-theory for certain primitive quotients of A.

Phase calculations for planar partition polynomials

In the study of the asymptotic behavior of polynomials from partition theory, the determination of their leading term asymptotics inside the unit disk depends on a sequence of sets derived from comparing certain complexvalued functions constructed from polylogarithms, functions defined as

Representation theory of U1 (H) in the symmetric tensors

Abstract The representations of the group of unitary operators which are trace-class perturbations of the identity on an infinite-dimensional separable Hilbert space are classified according to factoriality, quasi-equivalence, and semifiniteness, by relating these representations to the quasi-free representations of the Weyl algebra. This answers the problem posed by Ş. Strǎtilǎ and D. Voiculescu (Lecture Notes in Mathematics, Vol. 486, Springer-Verlag, Berlin/New York, 1975 ).

PERIODIC ATTRACTORS OF RANDOM TRUNCATOR MAPS

This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdts spin market model.

Panoramic Image Processing using Non-Commutative Harmonic Analysis Part I: Investigation

Automated surveillance, navigation and other applications in computational vision have prompted the need for omnidirectional imaging devices and processing. Omnidirectional vision involves capturing and interpreting full 360° panoramic images using rotating cameras, multiple cameras or cameras coupled with mirrors. Due to the enlarged field of view and the type of sensors required, typical techniques in image analysis generally fail to provide sufficient results for feature extraction and identification. A non-commutative harmonic analysis approach takes advantage of the Fourier transform properties of certain groups. Past work in representation theory already provides the theoretical background to analyze 2-D images though extensive numerical work for applications is limited. We will investigate the implementation and computation of the Fourier transform over groups, such as the motion group. The Euclidean motion group SE(2) is a solvable Lie group that requires a 2-D polar FFT and has symmetry properties that could be used as a tool in processing panoramic images.