We show that the representation, introduced by Lawrence and Krammer to show the linearity of Braid groups, is generically irreducible, but for that for some values of its two parameters when these are specialized to complex numbers , it becomes reducible. To do so, we construct a representation of degree n(n−1) 2 of the BMW algebra of type A n−1 inside the Lawrence-Krammer space. As a represent...

Let π = ⊗ p≤∞ πp be a cuspidal automorphic representation of GL(n) over Q. The adelic representation π is composed of π∞, an archimedean representation of GL(n,R), and nonarchimedean representations πp of GL(n,Qp) for each prime p. For all places p < ∞ outside of a finite set S, πp is unramified and parameterized by principal series parameters {αp,j}. Letting Ap ∈ GL(n,C) denote the diagonal ma...

      The French law, contrary to the Iranian law, has given the mother a kind of representation for guardianship and training of the child. This is a development that was established in France in 1970, and in Article 6 of the Iranian Family Protection Act of 2012, the granting of representation to the mother over the legal procedure for demand of the child or the incompetent has been entrusted...