Related papers: A faster method to construct extraspecial normalis…

We present a geometric formulation of $(p,q)$-strings in which the $Sl(2;Z)$-doublet of the two-form gauge potentials is constructed as second order in the supersymmetric currents. The currents are constructed using a supergroup manifold…

In the case of Uq(sl(2,R)) at root of unity q-deformed analogues are proposed for the generator of the maximal compact subalgebra, J, and for the raising and lowering operators. We prove an algebraic identity which implies that J has…

We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of…

It is shown how to use as horizontal symmetry the dicyclic group $Q_6 \subset SU(2)$ in a supersymmetric unification $SU(5)\otimes SU(5)\otimes SU(2)$ where one $SU(5)$ acts on the first and second families, in a horizontal doublet, and the…

We prove that the groups PSL_n(q) are (2,3)-generated for n=9,10 or 11 and all q. Actually, we find out explicit generators x_n and y_n of respective orders 2 and 3, for the groups SL_n(q).

The purpose of this paper is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on $\Vert…

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of…

In this paper, we construct, for some $2$-groups $G$, explicit Galois extensions $E/\mathbb{Q}(T)$ of group $G$ with $E\cap\overline{\mathbb{Q}}=\mathbb{Q}$. We also provide explicit arithmetic progressions of integers $t_0$ such that the…

This article produces a complete list of all maximal subgroups of the finite simple groups of type $F_4$, $E_6$, and twisted $E_6$ over all finite fields. Along the way, we determine the collection of Lie primitive almost simple subgroups…

We construct log-modular quantum groups at even order roots of unity, both as finite-dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de-equivariantization procedure. The existence of such quantum groups…

We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group $\bar{U}_{q}(\mathfrak{sl}_{2})$. This is a diagrammatic description of…

For each integer \( n \geq 3 \), we construct a self-dual regular 3-polytope \( \mathcal{P} \) of type \( \{n, n\} \) with \( 2^n n \) flags, resolving two foundamental open questions on the existence of regular polytopes with certain…

In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…

We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…

We describe the quasitriangular structure (universal $R$-matrix) on the non-standard quantum group $U_q(H_1,H_2,X^\pm)$ associated to the Alexander-Conway matrix solution of the Yang-Baxter equation. We show that this Hopf algebra is…

We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…

We consider local unitary invariants and entanglement monotones for the mixed two qutrit system. Character methods for the local SU(3)xSU(3) transformation group are used to establish the count of algebraically independent polynomial…

We introduce a new method for constructing complex-valued $r$-harmonic functions on Riemannian manifolds. We then apply this method for the important semisimple Lie groups $SO(n)$, $SU(n)$, $Sp(n)$, $SL_n(R)$, $Sp(R,n)$, $SU(p,q)$,…

In this short note, we prove that for $\mathcal{E} \subset \mathbb{F}_q^d$ with $|\mathcal{E}| \geq q^{d-1} + O(q^2)$ then the set of determinants generated by $\mathcal{E}$ is $\mathbb{F}_q.$ This result is nearly optimal and generalizes…

For an odd prime p, we determine a minimal set of topological generators of the pro-p Iwahori subgroup of a split reductive group G over Z\_p. In the simple adjoint case and for any sufficiently large regular prime p, we also construct…