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A proof of the level 1 and small weight cases of the conjecture was obtained in 2004 by Chandrashekhar Khare and Jean-Pierre Wintenberger, [3] and by Luis Dieulefait, [4] independently. In 2005, Chandrashekhar Khare obtained a proof of the level 1 case of Serre conjecture, [ 5 ] and in 2008 a proof of the full conjecture in collaboration with ...
Representation theory is a branch of ... especially conformal field theory and the theory of exactly solvable models. Kac discovered an elegant proof of ...
These operators are complicated, and one would like to find a simpler representation, which can be used to generate approximate calculational schemes. The transformation was developed [1] in 1940 by Theodore Holstein, a graduate student at the time, [2] and Henry Primakoff. This method has found widespread applicability and has been extended in ...
The Kolmogorov–Arnold representation theorem is closely related to Hilbert's 13th problem.In his Paris lecture at the International Congress of Mathematicians in 1900, David Hilbert formulated 23 problems which in his opinion were important for the further development of mathematics. [7]
Birkhoff's HSP theorem states that every model of an algebra A is the homomorphic image of a subalgebra of a direct product of copies of A. [ 3 ] In the study of semigroups , the Wagner–Preston theorem provides a representation of an inverse semigroup S , as a homomorphic image of the set of partial bijections on S , and the semigroup ...
The real part of is a continuous real linear functional on and so the Riesz representation theorem may be applied to := and the associated real Hilbert space (, ,, ) to produce its Riesz representation, which will be denoted by .
By Stone's representation theorem for Boolean algebras there is a ... An example of an influential proof from geometric model theory is Hrushovski's proof of the ...
The (0, 0) representation is the one-dimensional trivial representation and is carried by relativistic scalar field theories. Fermionic supersymmetry generators transform under one of the (0, 1 / 2 ) or ( 1 / 2 , 0) representations (Weyl spinors).