We determine the commutative Schur rings over S6 that contain the sum of all the transpositions in S6. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring. 2010 MSC: 20C05, 20F55

Using a new classification of 2-generator p-groups of class 2, we compute various homological functors for these groups. These functors include the nonabelian tensor square, nonabelian exterior square and the Schur multiplier. We also determine which of these groups are capable and which are unicentral.

The aim of this paper is to give a unified comparison of non-overlapping domain decomposition methods (DDMs) for solving magnetic field problems. The methods under investigation are the Schur complement method and the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method, and their solvers. The performance of these methods has been investigated in detail for two-dim...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CHAPTER 1. HISTORICAL BACKGROUND . . . . . . . . . . . . . . . . . 1 1.1 Early Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Resolvent Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 More Recent Developments . . . . . . . . . . . . . . . . . ....

This paper concerns the applications of Schur ring theory to the isomorphism problem of circulant graphs (Cayley graphs over cyclic groups). A digest of the most important facts about Schur rings presented in the first sections provides the reader with agentie self-eontained introduction to this area. The developed machinery allows us to give proofs of two eonjectures (Zibin' 1975 and Toida 197...

Let W be a finite Weyl group and σ a non-trivial graph automorphism of W . We show a remarkable relation between the σ-twisted involution module for W and the Frobenius–Schur indicators of the unipotent characters of a corresponding twisted finite group of Lie type. This extends earlier results of Lusztig and Vogan for the untwisted case and then allows us to state a general result valid for an...

We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also dis...

Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$ to case $q=1$, ${\mathcal{Q}(n,r)}$ is obtained. In this article, we reconstruct universal enveloping algebra ${U({\mathfrak{q}_n})}$ of Lie ${\mathfrak{q}_n}$ via ${\mathcal{Q}(n,r)}$, and achieve another explanation Schur-Weyl-Sergeev duality. Finally, depict duality over $\mathbb{Z}$.