Related papers: Group and round quadratic forms

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…

In this note, we construct explicit examples of $F_Q$-minimal quadratic forms of dimension $5$ and $7$, where $F_Q$ is the function field of a conic over a field $F$ of characteristic $2$. The construction uses the fact that any set of $n$…

We study linkage of $(d+1)$-fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension $d$. Specifically, we characterise this property in terms of linkage of quadratic…

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…

We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…

Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms. This is obtained from a more…

Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two…

We classify all possible extensions of a valuation from a ground field $K$ to a rational function field in one or several variables over $K$. We determine which value groups and residue fields can appear, and we show how to construct…

In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known…

We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. We also construct point…

We study quadratic form parameters $Q$ over the integers and extended quadratic forms with values in $Q$, which we call $Q$-forms. Certain form parameters $Q$ appeared in Wall's work on the classification of almost closed $(n-1)$-connected…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…

In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. to representation theory and irreducible representations of the Poincar'e group. Also, we tried to get a more comprehensible…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

We present a complete suite of algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic different from 2. This is a new version with numerous changes and improvements.

This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…

In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…