If G is any finite product of orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G. If G is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of G are enough. This extends a result of A. Sengupta [7]. In partic...

this work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $ax = b$ and $xc = d$ with orthogonal constraint. by optimal correction approach, a general representation of the orthogonal solution is obtained. this method is tested on two examples to show that the optimal correction is eective and highly accurate.

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

Orthogonal polynomials on the standard simplex Σ in R are shown to be related to the spherical orthogonal polynomials on the unit sphere S in R that are invariant under the group Z2×· · ·×Z2. For a large class of measures on S cubature formulae invariant under Z2 × · · · × Z2 are shown to be characterized by cubature formulae on Σ. Moreover, it is also shown that there is a correspondence betwe...

There are many different methods to obtain an orthogonal matrix. Householder discovered an orthogonal matrix, and it can be applied to solve physical problems of reflection. In this classroom note, we can obtain an orthogonal matrix group eAt, where A is antisymmetric with angular vector ω. When t is setting to be t=π/|ω|, eAt is equivalent to a Householder matrix of a reflecting plane with nor...

where X is an m x n matrix (m > n) in terms of p-adic solutions to (1.1) (or equivalently, solutions of (1.1) as a congruence). Let G be the orthogonal group O(A). Now G acts on the variety V consisting of solutions of (1.1). G(R) acts transitively on V(R) and the stabilizer He of V is an orthogonal group in rn n variables. V(R) carries a normalized G(R)-invariant measure # coming from the Hard...

In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we c...

We prove that the quantum group inclusion On ⊂ O ∗ n is “maximal”, where On is the usual orthogonal group and O ∗ n is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum group On ⊂ G ⊂ O ∗ n . In order to prove this result, we use: (1) the isomorphism of projective versions PO∗ n ≃ PUn, (2) some maximality results for classical groups, obtain...

In this paper, we construct three ternary linear codes associated with the orthogonal group O − (2, q) and the special orthogonal groups SO − (2, q) and SO − (4, q). Here q is a power of three. Then we obtain re-cursive formulas for the power moments of Kloosterman sums with square arguments and for the even power moments of those in terms of the frequencies of weights in the codes. This is don...