In group theory, an isotypical, primary or factor representation of a group G is a unitary representation π : G ⟶ B ( H ) {\displaystyle \pi :G\longrightarrow...
3 KB (308 words) - 17:50, 1 January 2024
representations Isotypical representation Representation theory of SL2(R) Representations of the Lorentz group Stone–von Neumann theorem Unitary representation of...
7 KB (1,003 words) - 14:58, 15 March 2025
specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group...
24 KB (4,081 words) - 03:48, 19 May 2025
refer to the section on direct sums of representations. A representation is called isotypic if it is a direct sum of pairwise isomorphic irreducible representations...
105 KB (21,294 words) - 10:21, 1 April 2025
the isotypic component of A of trivial type. 2. The isotypic decomposition of a semisimple representation is the decomposition into the isotypic components...
34 KB (5,011 words) - 21:43, 4 September 2024
In mathematics, a representation on coordinate rings is a representation of a group on coordinate rings of affine varieties. Let X be an affine algebraic...
4 KB (672 words) - 04:03, 6 March 2025
Hecke algebra of a finite group (category Representation theory of Lie groups)
each irreducible representation W {\displaystyle W} of G, the action of H on V preserves W ~ {\displaystyle {\tilde {W}}} – the isotypic component of W...
2 KB (340 words) - 01:15, 15 May 2024
observables. A unitary representation of O may be decomposed as the direct sum of irreducible unitary representations of O. Each isotypic component in this...
16 KB (2,429 words) - 10:27, 2 April 2025
The Classical Groups (category Representation theory)
covariant) variables for a standard classical group action; second, the isotypic decomposition of the full tensor algebra for such an action. 1Most people...
4 KB (495 words) - 20:29, 9 June 2022
algebra and the exterior algebra appear as the isotypical components of the trivial and sign representation of the action of S n {\displaystyle S_{n}} acting...
13 KB (2,050 words) - 23:04, 2 March 2025
include the ring of n × n real square matrices with n ≥ 2, group rings in representation theory, operator algebras in functional analysis, rings of differential...
99 KB (13,697 words) - 09:39, 16 June 2025
300 AD in China. This was likely to be a liquid colloid of gold. Leonite is isotypic with the mineral mereiterite (K2Fe(SO4)2·4H2O), and with artificial Mn-leonite...
28 KB (3,014 words) - 02:25, 27 May 2025