Let Λ be a ring endowed with an involution a 7→ ã. We say that two units a and b of Λ fixed under the involution are congruent if there exists an element u ∈ Λ× such that a = ubũ. We denote by H(Λ) the set of congruence classes. In this paper we consider the case where Λ is an order with involution in a semisimple algebraA over a local field and study the question whether the natural map H(Λ)→ ...

Let f : X → Spec(Z) be an arithmetic variety of dimension d ≥ 2 and (H, k) an arithmetically ample Hermitian line bundle on X, that is, a Hermitian line bundle with the following properties: (1) H is f -ample. (2) The Chern form c1(H∞, k) gives a Kähler form on X∞. (3) For every irreducible horizontal subvariety Y (i.e. Y is flat over Spec(Z)), the height ĉ1( (H, k)|Y ) dim Y of Y is positive. ...

Let M be a 2n dimensional smooth closed oriented manifold. Let g be a Riemmian metric on TM and ∇ the associated Levi-Civita connection. Let V be a complex vector bundle over M with a Hermitian metric h and a unitary connection ∇ . Let ΛC(T ∗M) be the complexified exterior algebra bundle of TM and let 〈 , 〉ΛC(T∗M) be the Hermitian metric on ΛC(T ∗M) induced by g . Let dv be the Riemannian volum...

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...

We obtain a technique to reduce the computational complexity associated with decoding of Hermitian codes. In particular, we propose a method to compute the error locations and values using an uni-variate error locator and an uni-variate error evaluator polynomial. To achieve this, we introduce the notion of Semi-Erasure Decoding of Hermitian codes and prove that decoding of Hermitian codes can ...

Canonical forms for matrix triples (A,G, Ĝ), where A is arbitrary rectangular andG, Ĝare either real symmetric or skew symmetric, or complex Hermitian or skew Hermitian, arederived. These forms generalize classical singular value decompositions. In [1] a similarcanonical form has been obtained for the complex case. In this paper, we provide analternative proof for the comple...

Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 3 and standard module V . Recently Ito and Terwilliger introduced four direct sum decompositions of V ; we call these the (μ, ν)–split decompositions of V , where μ, ν ∈ {↓, ↑}. In this paper we show that the (↓, ↓)–split decomposition and the (↑, ↑)–split decomposition are dual with respect to the standard Hermitian form on V...

Let f! = G/K be a symmetric tube domain where G is the universal cover of Aut(f!). Let X be a line bundle on the Shilov boundary, and let I(x) be the space of sections. This paper determines (a) the composition series for I(x) as a ({1, K)module, (b) the K-module structure of each constituent, (c) explicit formulas for possible invariant Hermitian forms on these constituents, and (d) the unitar...

For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables Oα of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian q...

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