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Unitary Groups, Unitary Steinberg Groups, and Unitary K-Groups
1989This chapter presents a theory of unitary groups over rings parallel to that which Chapter 1 develops for the linear groups. We will introduce the concept of a form ring which will allow for the definition of generalized quadratic forms. The unitary groups — i.e.
O. Timothy O’Meara, Alexander J. Hahn
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Unitary representations of the unitary group
Mathematical Proceedings of the Cambridge Philosophical Society, 1969It is well known that every representation of the group Un of unitary matrices of order n × n is equivalent to a unitary representation (see e.g. Little-wood (6), ch. XI). Our object in the present paper is to discuss some properties of those representations, and to construct a specific unitary representation.
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, 1990
An MCSCF method based on a restricted active space (RAS) type wave function has been implemented. The RAS concept is an extension of the complete active space (CAS) formalism, where the active orbitals are partitioned into three subspaces: RAS1, which ...
P. Malmqvist +2 more
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An MCSCF method based on a restricted active space (RAS) type wave function has been implemented. The RAS concept is an extension of the complete active space (CAS) formalism, where the active orbitals are partitioned into three subspaces: RAS1, which ...
P. Malmqvist +2 more
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The Annals of Mathematics, 1964
The purpose of this paper is to develop the theory of elementary divisors, to prove the approximation theorem, and to determine the class number for the following two types of algebraic groups: (i) the unitary group of a hermitian form over an algebraic number field; (ii) the unitary group of a hermitian form over a quaternion algebra, having an ...
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The purpose of this paper is to develop the theory of elementary divisors, to prove the approximation theorem, and to determine the class number for the following two types of algebraic groups: (i) the unitary group of a hermitian form over an algebraic number field; (ii) the unitary group of a hermitian form over a quaternion algebra, having an ...
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Journal of Physical Chemistry A, 2009
A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has
Wanyi Jiang, Y. Khait, M. Hoffmann
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A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has
Wanyi Jiang, Y. Khait, M. Hoffmann
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, 2009
Improved procedures were used in a new computer implementation of the graphical unitary group approach, designed specifically for efficient multireference configuration interaction calculations for molecules.
H. Lischka +3 more
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Improved procedures were used in a new computer implementation of the graphical unitary group approach, designed specifically for efficient multireference configuration interaction calculations for molecules.
H. Lischka +3 more
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K-Theory, 2003
Overgroups of the elementary hyperbolic unitary group over a form ring subject to a stability condition which holds in particular for almost commutative and semilocal rings, are described.
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Overgroups of the elementary hyperbolic unitary group over a form ring subject to a stability condition which holds in particular for almost commutative and semilocal rings, are described.
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Graph theoretical concepts for the unitary group approach to the many-electron correlation problem
, 2009The simplified unitary group formalism for electronic states introduced by Paldus was recast in a form based on a relatively small table of ''distinct rows'' of the array (or tableau) representatives of the appropriate canonical basis functions.
I. Shavitt
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Journal of Physics A: Mathematical and General, 1980
The subjoining of one compact Lie group H to another such group G is discussed with particular reference to the cases for which G=U(N) and H=U(n). It is shown that maximal subjoinings of these unitary groups are specified by means of the monomial symmetric functions. Subjoinings, which are defined in terms of mappings between weight spaces, are studied
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The subjoining of one compact Lie group H to another such group G is discussed with particular reference to the cases for which G=U(N) and H=U(n). It is shown that maximal subjoinings of these unitary groups are specified by means of the monomial symmetric functions. Subjoinings, which are defined in terms of mappings between weight spaces, are studied
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A unitary group formulation of open‐shell electron propagator theory
, 2009By replacing the usual annihilation and creation operators of second quantization by appropriately normalized fundamental Wigner operators of the unitary group U(n) and by representing the many‐electron spin eigenfunctions in terms of the Gelfand–Tsetlin
G. Born, I. Shavitt
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