Related papers: Characters of real special 2-groups
It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields…
We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.
Using the \texttt{WeylModules} \textsf{GAP} Package, we compute structural information about certain Weyl modules for type $G_2$ in characteristic $2$. This gives counterexamples to two conjectures stated by S.~Donkin in 1990. It also…
In this paper we characterize all of Cayley graphs on dihedral groups with metric dimension two.
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
In this paper, we determine the 2-rank of the class group of certain classes of real cyclic quartic number fields. Precisely, we consider the case in which the quadratic subfield is Q(\sqrt{l}) with l=2 or a prime congruent to 1 mod 8.
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.
We classify degenerate singular points of $\C^2$-actions on complex surfaces.
We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an…
We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant…
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
For simple algebraic groups defined over algebraically closed fields of good characteristic, we give upper bounds on the covering numbers of unipotent conjugacy classes in terms of their (co)ranks and in terms of their dimensions.
The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…
We apply the theory of branches in Bruhat-Tits trees, developed in previous works by the second author and others, to the study of two dimensional representations of finite groups over the ring of integers of a number field. We provide a…
For $\mathrm{O}(\mathrm{q},k)$, the orthogonal group over a field $k$ of characteristic 2 with respect to a quadratic form $\mathrm{q}$, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either…
We check McKay conjecture on character degrees for the case of symplectic groups over the field with two elements Sp(2n,2) and the prime 2. Then we check the inductive McKay condition (Isaacs-Malle-Navarro 2007) for Sp(4,2^m) and all…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…