Abstract Let G be a compact connected Lie group, and let $\operatorname {Hom}({\mathbb {Z}}^m,G)$ the space of pairwise commuting m -tuples in . We study problem which primes $p \operatorname {Z}}^m,G)_1$ , component containing element $(1,\ldots ,1)$ has p -torsion homology. will prove that for $m\ge 2$ homology if only divides order Weyl group $G=SU(n)$ some exceptional groups. also compute t...

THE EXCEPTIONAL SIMPLE LIE ALGEBRAS F4 AND E6 By CLAUDE CHEVALLEY AND R. D. SCHAFER DEPARTMENTS OF MATHEMATICS, COLUMBIA UNIVERSITY AND UNIVERSITY OF PENNSYLVANIA Communicated by A. A. Albert, December 28, 1949 Let K be an algebraically closed field of characteristic 0. The exceptional simple Jordan algebra 3 over K is the (non-associative) algebra of dimension 27 whose elements are 3 X 3 Hermi...

UCSD/PTH 98–11 We complete the process of classifying all supersymmetric theories with quantum modified moduli. We present all the supersymmetric gauge theories based on a simple orthogonal or exceptional group that exhibit a quantum modified moduli space. The quantum modified constraints of theories derived from s-confining theories are invariant under all symmetries. However, theories that ca...

In this paper we advance the program of using exceptional collections to understand the gauge theory description of a D-brane probing a Calabi-Yau singularity. To this end, we strengthen the connection between strong exceptional collections and fractional branes. To demonstrate our ideas, we derive a strong exceptional collection for every Y p,q singularity, and also prove that this collection ...

We study representations of simple alternative superalgebras B(1, 2) and B(2, 4). The irreducible bimodules and bimodules with superinvolution over these superalgebras are classified, and some analogues of the Kronecker factorization theorem are proved for alternative superalgebras that contain B(1, 2) and B(4, 2).