We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

The polarized T Gowdy model is, in a standard gauge, characterized by a point particle degree of freedom and a scalar field degree of freedom obeying a linear field equation on R × S. The Fock representation of the scalar field has been well-studied. Here we construct the Schrödinger representation for the scalar field at a fixed value of the Gowdy time in terms of square-integrable functions o...

A classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integr...

A classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integr...

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data obtained in [15] and [19]. The second aim of the paper is to give description of an invariant (partially defined function) of irreducible square integrable r...

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) x J&, embedded into the Lorentz group S00(3, 1) via the Iwasawa decomposition, and X Y SO,(3,1)/C. The space L2(S2, a!~) carries a unitary irreduci...

I will first formulate a problem in the theory of group representations and show how to solve it; then I will discuss the relation of this problem to the theory of automorphic forms. Since there is no point in striving for maximum generality, I start with a connected semisimple group G with finite center. An irreducible unitary representaiton π of G on the Hilbert space H is said to be square-i...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...