Related papers: On the Mathieu conjecture for $SU(2)$
The McCarty Conjecture states that any McCarty Matrix (an $n\times n$ matrix $A$ with positive integer entries and each of the $2n$ row and column sums equal to $n$), can be additively decomposed into two other matrices, $B$ and $C$, such…
The linear delta expansion is applied to a calculation of the SU(2) mass gap on the lattice. Our results compare favourably with the strong-coupling expansion and are in good agreement with recent Monte Carlo estimates.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We consider non-trivial irreducible tensor products of modular representations of a symmetric group $S_n$ in characteristic 2 for even $n$ completing the proof of a classification conjecture of Gow and Kleshchev about such products.
We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights,…
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
The SU(2) invariant massive Thirring model with a boundary is considered on the basis of the vertex operator approach. The bosonic formulae are presented for the vacuum vector and its dual in the presence of the boundary. The integral…
Scalar particles in the adjoint representation of a non-Abelian gauge theory play an important role in many scenarios beyond the standard model, especially of GUT type. For such theories manifestly gauge-invariant, massless, composite…
In this paper we discuss a general framework in which we present a new conjecture, due to Wenhua Zhao, the Image Conjecture. This conjecture implies the Generalized Vanishing Conjecture and hence the Jacobian Conjecture. Crucial ingredient…
The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators,…
Sufficient conditions for the relation $tan \beta \simeq m_t/m_b$ to hold in supersymmetric grand unified theories are formulated. Essential ingredients are the $SU(2)_R$ gauge symmetry and a discrete matter parity. The applicability of our…
In this paper we propose a conjecture about integer solutions to any equations, based on Primal algebra specifically this conjecture is a corollary of the Acu\~na Theorem in that article. Also some problems are proposed which, if the…
In this paper we announce a conjecture concerning enumeration of 2n x k n-times persymmetric matrices over F_2 by rank.
An analysis of a $SU(2)_L \times SU(2)_R$ invariant, supersymmetric effective theory is given. The resulting leading and next to leading independent invariants are stated in terms of the underlying Killing vectors and K\"ahler potential.…
Principal axis transformation is performed for a Lagrangian with a U(1)-SU(2) mixing term, that can cause a SU(2) deconfining transition.
We prove two determinant evaluations attached to Sun's conjectures on matrices of Legendre symbols. The first one resolves the \(p\equiv1\pmod4\) part of Conjecture 4.8(i) by reducing the determinant with four indeterminates to a four-entry…
In this paper, we study combinatorics of congruence subgroups of the modular group. More precisely, we consider the matrix equation that naturally arises in the theory of Coxeter friezes and investigate its irreducible solutions. We give…
Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
We give a detailed description of the adjoint representation of Drinfeld's twist element, as well as of its coproduct, for $su_{q}(2)$. We also discuss, as applications, the computation of the universal R-matrix in this representation and…