On the Order of the Unitary Subgroup of Modular Group Algebra

Some bounds on unitary duals of classical groups‎ - ‎non-archimeden case

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

Solvable $L$-subgroup of an $L$-group

In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

OD-characterization of $U_3(9)$ and its group of automorphisms

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras