N ov 2 00 1 Applications of Commutator - Type Operators to p - Groups ∗

1 3 N ov 2 00 6 Recent developments in applied pseudoanalytic function theory

We present recently obtained results in the theory of pseudoanalytic functions and its applications to elliptic second-order equations. The operator (div p grad +q) with p and q being real valued functions is factorized with the aid of Vekua type operators of a special form and as a consequence the elliptic equation (div p grad +q)u = 0, (1) reduces to a homogeneous Vekua equation describing ge...

N ov 2 00 5 FOURIER TRANSFORMS RELATED TO A ROOT SYSTEM OF RANK 1

We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C ∨ 1 , C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric v...

ar X iv : m at h - ph / 0 11 10 07 v 1 5 N ov 2 00 1 FREDHOLM DETERMINANTS , JIMBO - MIWA - UENO TAU - FUNCTIONS , AND REPRESENTATION THEORY

The authors show that a wide class of Fredholm determinants arising in the representation theory of " big " groups such as the infinite–dimensional unitary group, solve Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann–Hilbert problems.

ar X iv : h ep - t h / 04 11 21 1 v 1 2 3 N ov 2 00 4 Dirac quantization of a nonminimal gauged O ( 3 ) sigma model

The (2+1) dimensional gauged O(3) nonlinear sigma model with Chern-Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of constraints of the model is modified by the introduction of the Pauli coupling. Moreover, we found that the quantum commutator relations in the nominimal case is i...

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions