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Maximum likelihood from incomplete data via the EM algorithm
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1977
"... A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situat ..."
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Cited by 11972 (17 self)
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situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
ON REGULARITY OF FINITE REFLECTION GROUPS
"... Abstract. We define a concept of “regularity ” for finite unitary reflection groups, and show that an irreducible finite unitary reflection group of rank greater than 1 is regular if and only if it is a Coxeter group. Hence we get a characterization of Coxeter groups among all the irreducible finite ..."
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Abstract. We define a concept of “regularity ” for finite unitary reflection groups, and show that an irreducible finite unitary reflection group of rank greater than 1 is regular if and only if it is a Coxeter group. Hence we get a characterization of Coxeter groups among all the irreducible
THE REPRESENTATIONS OF FINITE REFLECTION GROUPS
"... Abstract. The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G. D. James. Halıcıoğlu and Morris describe a possible extension of James ’ work for Weyl groups in general, ..."
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, where Young tableaux are interpreted in terms of root systems. In this paper, we further develop the theory and give a possible extension of this construction for finite reflection groups which cover the Weyl groups. 1.
UNIFORMIZATION OF THE ORBIFOLD OF A FINITE REFLECTION GROUP
"... We try to understand the relationship between the K(π, 1)property of the complexified regular orbit space of a finite reflection group and the flat structure on the orbit space via the uniformization equation attached to the flat structure. ..."
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Cited by 14 (4 self)
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We try to understand the relationship between the K(π, 1)property of the complexified regular orbit space of a finite reflection group and the flat structure on the orbit space via the uniformization equation attached to the flat structure.
SEPARATING INVARIANTS AND FINITE REFLECTION GROUPS
, 2008
"... Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a more geometric notion of separating algebra. This allows us to prove that when there is a pol ..."
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Cited by 9 (5 self)
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polynomial separating algebra, the group is generated by reflections, and when there is a complete intersection separating algebra, the group is generated by bireflections.
Semiinvariants of finite reflection groups
 J. of Algebra
, 1999
"... Abstract. Let G be a finite group of complex n×n unitary matrices generated by reflections acting on C n. Let R be the ring of invariant polynomials, and χ be a multiplicative character of G. Let Ω χ be the Rmodule of χinvariant differential forms. We define a multiplication in Ω χ and show that u ..."
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Cited by 7 (3 self)
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Abstract. Let G be a finite group of complex n×n unitary matrices generated by reflections acting on C n. Let R be the ring of invariant polynomials, and χ be a multiplicative character of G. Let Ω χ be the Rmodule of χinvariant differential forms. We define a multiplication in Ω χ and show
SPECHT MODULES FOR FINITE REFLECTION GROUPS
, 2003
"... Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A Young, and of irreducible modules, called Specht modules, due to W Specht, for the symmetric groups Sn which are based on elegant combinatorial concepts connected with Young tableaux e ..."
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Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A Young, and of irreducible modules, called Specht modules, due to W Specht, for the symmetric groups Sn which are based on elegant combinatorial concepts connected with Young tableaux
The DonaldFlanigan problem for finite reflection groups
"... To the memory of Moshé Flato, z”l Abstract. The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types Bn and Dn (whose rational group algebras are compu ..."
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Cited by 3 (0 self)
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are computed), leaving but six finite reflection groups with solutions unknown. We determine the structure of a wreath product of a group with a sum of central separable algebras and show that if there is a solution for H over k which is a sum of central separable algebras and if Sn is the symmetric group
Finite reflection groups and linear preserver problems
 Rocky Mountain J. of Mathematics
, 2001
"... naturally acting on a Euclidean space V, and let L(G) stand for the set of linear transformations φ of EndV that satisfy φ(G) = G. It is easy to see that L(G) contains all transformations of the form X 7→ PXQ, X 7 → PX∗Q, where P,Q belong to the normalizer of G in the orthogonal group and PQ ∈ G. W ..."
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Cited by 4 (3 self)
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naturally acting on a Euclidean space V, and let L(G) stand for the set of linear transformations φ of EndV that satisfy φ(G) = G. It is easy to see that L(G) contains all transformations of the form X 7→ PXQ, X 7 → PX∗Q, where P,Q belong to the normalizer of G in the orthogonal group and PQ ∈ G
Results 1  10
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