The theory has been widely applied in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book Gruppentheorie und Quantenmechanik. One of the pioneers in constructing a general theory of unitary representations, for any group G rather than just for particular groups useful in applications, was George Mackey.
Context in harmonic analysis
The theory of unitary representations of groups is closely connected with harmonic analysis. In the case of an abelian group G, a fairly complete picture of the representation theory of G is given by Pontryagin duality. In general, the unitary equivalence classes (see below) of irreducible unitary representations of G make up its unitary dual. This set can be identified with the spectrum of the C*-algebra associated to G by the group C*-algebra construction. This is a topological space.
"Vanity, and chase of wind!" ...Ever since the nation started seriously considering the restiveness of Muslim Mindanao and its just claims for autonomy, then we had to seriously think of an alternative to the unitary system to which history wedded us. The concept of "proportional representation" that many of us did not initially grasp was introduced.
In contrast, a unitary government would guarantee proportional representation and the universal protection of the rights of all citizens, without the contradiction between local, provincial, and national governance ... The most obvious objection to this proposal is that a unitary ...
Whereas, the efforts of the All Ceylon Tamil Congress to ensure non-domination of the minorities by the majority by the adoption of a scheme of balanced representation in a Unitary Constitution have failed and even the meagre safeguards provided in article 29 of the Soulbury...
The research demonstrates new competitors enlisted in the global Unitary Material market report ... The report on the global Unitary Material market has been designed to help readers to understand tables and graphical representation related to the specific industry to boost their business sphere on the international platform.
The world-renowned platform of Blockchain technology, FLETA, has entered into a partnership contract with the decentralized ecosystem of data sharing that is GeoDB. Founded by GeoDB Blockchain Limited, GeoDB is a company based in London... The GeoDB token is a unitary representation of the market value of big data in the ecosystem of GeoDB. Tags ... ....
They have been able to monopolize decision-making because even our post Martial Law constitution of 1987 does not guarantee proportionate representation in government to all sectors of society ... It does not matter what form (unitary or federal) government takes either.
Trichy...Shai Evra was chosen for his outstanding work on high dimensional expanders in the area of combinatorial and geometric topology, and on “Golden Gates” for three dimensional unitary groups. The prize notes that he employs deep results from representation theory and number theory pertaining to the Generalized Ramanujan Conjectures ... Download ... .
In the early 60s, inspired by ideas of Andre Weil, Narasimhan and Seshadri began studying families of “irreducible unitary representations of the fundamental group of a Riemann surface”.
Nevertheless, certain countries have made "irresponsible comments and unwarranted accusations" against the NPC decision, meddling in Hong Kong affairs and China's internal affairs, Zhao said, adding the Chinese side has lodged stern representations with the countries.
Whereas, the efforts of the All Ceylon Tamil Congress to ensure non-domination of the minorities by the majority by the adoption of a scheme of balanced representation in a Unitary Constitution have failed and even the meagre safeguards provided in article 29 of the Soulbury...
// ... The proposal has been prepared with five objectives; the rebuilding of the civilizational state, true public representation and the sovereignty of the people, consolidation of a unitary Sri Lanka, and ensuring the balance between the executive, the legislature and the judiciary and to build a society which values responsibilities ... .
One important area of neglect pointed out by researchers and some commentators, is the lack of representation on board vessels. Historically, this representation has been provided by seafarers’ unions ... This is not surprising as it is often a given that employers prefer unitary approaches to managing businesses.
Unitary projects such as nationalism have strong homogenising tendencies that consider particular identities and their aspirations for representation irrelevant or even fissiparous ... Reddy believes that welfarism alone is not sufficient and representation is critical in the changed situation.