By Parker C.W., Wiedorn C.B.
Allow G be a in the neighborhood K-proper crew, S ∈ Syl_5(G), and Z = Z(S). We demonstratethat if is 5-constrained and Z isn't weakly closed in thenG is isomorphic to the monster sporadic easy team.
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Extra info for A 5-local identification of the monster
There is in fact a smaller supermultiplet, which we discard because it contains gravitini but no graviton states. Finally, we turn to the case of (N+ , N− ) = (2, 2). The smallest supermultiplet is given by the tensor product of the smallest (2, 0) and (0, 2) supermultiplets. This yields the 128 + 128 states of the (2, 2) supergravity multiplet. These states transform according to representations of U Sp(4) × U Sp(4). In principle, one can continue and classify representations for other values of (N+ , N− ).
However, conventional supergravity theories are not of this kind. e. in Table 5) to list supermultiplets with states transforming in higher-helicity representations. The fact that an inﬁnite number of ﬁelds can cure certain inconsistencies is by itself not new.
Table 9 reﬂects also the so-called periodicity theorem , according to which there exists an isomorphism between the Cliﬀord algebras C(p+8, q) (or C(p, q+8)) and C(p, q) times the 16 × 16 real matrices. Therefore, the dimension of the representations of C(p+8, q) (or C(p, q +8)) and C(p, q) diﬀers by a factor 16. Finally the table lists the branching of the Cliﬀord algebra representation into SO(p, q) spinor representations. When r = 0 the Cliﬀord algebra representation decomposes into two chiral spinors.
A 5-local identification of the monster by Parker C.W., Wiedorn C.B.