This alternate notational scheme is used primarily in verbal discussions or where a linear representation is desirable in print, but may also be permissible as during-game transcription by either or both players.
42.
In particular, if all V _ i's have spin 1 / 2 representation then the linear representation obtained from KZ equation agrees with the representation constructed from operator algebra theory by Vaughan Jones.
43.
It is known in particular that the direct sum decomposition of the regular representation contains a representative of every isomorphism class of irreducible linear representations of " G " over " K ".
44.
When considering subgroups of general Lie groups ( which are not necessarily defined as a matrix groups ) one has to use a linear representation of the group to take traces of elements.
45.
For example, the simple groups " A " 100 and SL 20 ( 2 ) are far larger, but easy to calculate with as they have " small " permutation or linear representations.
46.
Adults always say how Egyptian art looks modern, by which we really mean that modern art has evolved complicated forms of abstraction, symbolism and linear representation, many of which ultimately descend from the Egyptians.
47.
His 1958 monograph " Linear representations of the Lorentz group " helped to develop the theory of representations of the fundamental series of the complex classical groups, beginning with SL ( 2, C ).
48.
A linear representation of G into a Banach space V is defined to be a continuous group homomorphism of G into the set of all bijective bounded linear operators on V with a continuous inverse.
49.
One major mathematical application of the construction of spinors is to make possible the explicit construction of linear representations of the Lie algebras of the special orthogonal groups, and consequently spinor representations of the groups themselves.
50.
Because it does not handle leap seconds, it is neither a linear representation of time nor a true representation of UTC . Unix time may be checked on most Unix systems by typing on the command line.
