We develop a new approach for the computation of Mullineux involution symmetric group and its Hecke algebra using notion crystal isomorphism Iwahori-Matsumoto affine type \(A\). As consequence, we obtain several elementary combinatorial algorithms computation, one which is equivalent to Xu algorithm (and thus original algorithm). simple interpretation these proof that they indeed compute involu...

A symplectic involution on a K3 surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the CH0 group of the K3 surface, as predicted by Bloch’s conjecture. 2010 Mathematics Subject Classification: 14C25, 14J28

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes orders over definite, rational quaternion algebras orthogonal involution that admit such algorithm. give two applications: first, any order admits has class number 1; second, we show how existence relates to problem constructing explicit Dirichlet doma...

Let R be a commutative ring, G a group and RG its group ring. Let φ : RG → RG denote the R-linear extension of an involution φ defined on G. An element x in RG is said to be φantisymmetric if φ(x) = −x. A characterization is given of when the φ-antisymmetric elements of RG commute. This is a completion of earlier work. keywords: Involution; group ring; antisymmetric elements. keywords: 2000 Mat...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.