Related papers: Hensel's lemma for the norm principle for spinor g…

We here revisit Fourier analysis on the Heisenberg group H^d. Whereas, according to the standard definition, the Fourier transform of an integrable function f on H^d is a one parameter family of bounded operators on L 2 (R^d), we define (by…

For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

A comparison among different constructions of the quaternionic $4$-form $\Phi_{Sp(2)Sp(1)}$ and of the Cayley calibration $\Phi_{Spin(7)}$ shows that one can start for them from the same collections of "K\"ahler 2-forms", entering in…

The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth…

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass…

In his proof of the fundamental lemma, Ng\^o established the product formula for the Hitchin fibration over the anisotropic locus. One expects this formula over the larger generically regular semisimple locus, and we confirm this by…

We introduce a new family of norms on the permutation groups $S_{n}$. We examine their properties.

We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give…

This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…

- A hamiltonian graph $G$ verifying $e(G)>n(k-1)/2$ %with a vertex of degree greater or equal than $k$ contains any $k$-spider. - If $G$ is a graph with average degree $\bar{d} > k-1$, then every spider of size $k$ is contained in $G$ for…

We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…

The theory of slice regular functions is nowadays widely studied and has found its elegant applications to a functional calculus for quaternionic linear operators and Schur analysis. However, much less is known about their boundary…

We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fusion categories exist up to equivalence whose global…

For any finite reflection group $W$ on $\mathbb{R}^{N}$ and any irreducible $W$-module $V$ there is a space of polynomials on $\mathbb{R}^{N}$ with values in $V$. There are Dunkl operators parametrized by a multiplicity function, that is,…

In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division…

Let $\rho(\cdot)$ be the Koranyi norm on the Heisenberg group $\mathbb{H}^{n} \equiv (\mathbb{R}^{2n} \times \mathbb{R}, \, \cdot \, )$ defined by \[ \rho(x,t) = \left( |x|^{4} + 16 t^{2} \right)^{1/4}, \,\,\,\, (x,t) \in \mathbb{H}^{n}. \]…

Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. We show that any smooth model of the affine variety defined by the equation N_{K/Q} (k) = P(t) satisfies the Hasse…

We investigate the Cauchy--Szeg\H{o} projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy--Szeg\H{o} kernel and prove that the Cauchy--Szeg\H{o} kernel is non-zero…