complex reflection group 예문

예문모바일

So it is sufficient to classify the irreducible complex reflection groups.
By definition, every complex reflection group is generated by its reflections.
Complex reflection groups arise in the study of the invariant theory of polynomial rings.
Its complex reflection group is 3 [ 3 ] 3 [ 3 ] 3 or, order 648.
For more information, including diagrams, presentations, and codegrees of complex reflection groups, see the tables in.
Any complex reflection group is a product of irreducible complex reflection groups, acting on the sum of the corresponding vector spaces.
Any complex reflection group is a product of irreducible complex reflection groups, acting on the sum of the corresponding vector spaces.
A reducible complex reflection group is said to be well-generated if it is a product of irreducible well-generated complex reflection groups.
A reducible complex reflection group is said to be well-generated if it is a product of irreducible well-generated complex reflection groups.
The symmetry group of a regular complex polygon is not called a Coxeter group, but instead a Shephard group, a type of Complex reflection group.
The first has Complex reflection group 3 [ 5 ] 3, order 360, and the second has symmetry 5 [ 3 ] 5, order 600.
For irreducible well-generated complex reflection groups, the " Coxeter number " defined above equals the largest degree, h = d _ \ ell.
The corresponding notions can be defined over other fields, leading to "'complex reflection groups "'and analogues of reflection groups over a finite field.
The set of reflections is not a minimal generating set, however, and every irreducible complex reflection groups of rank has a minimal generating set consisting of either or reflections.
A complex reflection group " W " is "'irreducible "'if the only " W "-invariant proper subspace of the corresponding vector space is the origin.
Shephard and Todd proved that a finite group acting on a complex vector space is a complex reflection group if and only if its ring of invariants is a polynomial ring ( Chevalley Shephard Todd theorem ).
For any regular polytope the symmetry group ( here a complex reflection group, called a Shephard group ) acts transitively on the flags, that is, on the nested sequences of a point contained in a line contained in a plane and so on.
"' Tonny Albert Springer "'( 13 February 1926 7 December 2011 ) was a mathematician at Utrecht University who worked on linear algebraic groups, Hecke algebras, complex reflection groups, and who introduced Springer representations and the Springer resolution.
The triple cover of this group is a complex reflection group, 3 [ 3 ] 3 [ 3 ] 3 or of order 648, and the product of this with a group of order 2 is another complex reflection group, 3 [ 3 ] 3 [ 4 ] 2 or.
The triple cover of this group is a complex reflection group, 3 [ 3 ] 3 [ 3 ] 3 or of order 648, and the product of this with a group of order 2 is another complex reflection group, 3 [ 3 ] 3 [ 4 ] 2 or.