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Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
2015/9/29
Goldman gratefully acknowledges partial support by NSF grants
DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research
Award from the General Research Board of the University of
Maryland in Fa...
ANALYSIS ON COMPACT LIE GROUPS OF LARGE DIMENSION AND ON CONNECTED COMPACT GROUPS
LIE GROUPS LARGE DIMENSION
2015/8/26
The study of Gaussian convolution semigroups is a subject at the cross-
road between abstract and concrete problems in harmonic analysis. This article suggests
selected open problems that are in lar...
On Discretization of Tori of Compact Simple Lie Groups II
Discretization of Tori Compact Simple Lie Groups II Mathematical Physics
2012/6/14
The discrete orthogonality of special function families, called $C$- and $S$-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivn\'ak and Patera (2009 J...
On Isomorphism Testing of Groups with Normal Hall Subgroups
Group Isomorphism Problem Normal Hall Subgroups Computational Complexity
2012/12/3
A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur-Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a s...
CPT groups of higher spin fields
CPT groups fields on the Poincare group Clifford algebras automorphism groups higher spin fields
2011/9/16
Abstract: $CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz gr...
All the Groups of Signal Analysis from the (1+1)-affine Galilei Group
Signal Analysis the (1+1)-affine Galilei Group Mathematical Physics
2011/7/26
Abstract: We study the relationship between the (1+1)-affine Galilei group and four groups of interest in signal analysis and image processing, viz., the wavelet or the affine group of the line, the W...
The "boson polynomials" of Gel'fand basis and the analytic expression of Wigner's coefficients with multiplicity for the canonical basis of unitary groups
Gel'fand basis Wigner's coefficients canonical basis Representation Theory
2011/7/26
Abstract: In this paper we present the generating function method for the derivation of bosons polynomials of Gel'fand basis and Wigner coefficients for the canonical basis of SU(n). We find a new ana...
Branching of the W(H4) Polytopes and Their Dual Polytopes under the Coxeter Groups W(A4) and W(H3) Represented by Quaternions
Dual Polytopes the W(H4) Polytopes Quaternions
2011/7/26
Abstract: 4-dimensional H4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(H4) where the group elements and the vertices of the polytopes are represe...
Computations in Finite Groups and Quantum Physics
Computations Finite Groups Quantum Physics
2011/7/28
Abstract: Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observ...
Operator algebra quantum groups of universal gauge groups
Operator algebra quantum groups universal gauge groups
2010/12/24
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the conce...
Solitonic Models Based on Quantum Groups and the Standard Model
Solitonic Models Quantum Groups the Standard Model
2010/12/23
The idea that the elementary particles might have the symmetry of knots has had a long history. In any current formulation of this idea, however, the knot must be quantized. The present review is a su...
Conjugacy classes in Weyl groups and q-W algebras
Conjugacy classes Weyl groups q-W algebras
2010/12/27
We define noncommutative deformations W_q^s(G) of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group G which play the role of Slodowy sli...
The fractal structure of cellular automata on Abelian groups
Discrete Mathematics (cs.DM) Quantum Physics (quant-ph)
2010/11/8
It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structu...
Quantum 't Hooft loops of SYM N=4 as instantons of YM_2 in dual groups SU(N) and SU(N)/Z_N
Quantum 't Hooft loops SYM N=4 YM_2
2010/12/22
A relation between circular 1/2 BPS 't Hooft operators in 4d N=4 SYM and instantonic solutions in 2d Yang-Mills theory (YM_2) has recently been conjectured. Localization indeed predicts that those 't ...
Classical set theory is nonextensive since the mathematical definition of a set excludes the possibility that more than one copy of the same element can be in a set. We show that the description of ra...
