Related papers: Half-integral weight modular forms and application…

We propose a supersymmetric A4 x SU(5) model of quasi-degenerate neutrinos which predicts the effective neutrino mass m_ee relevant for neutrinoless double beta decay to be proportional to the neutrino mass scale, thereby allowing its…

We present a flavor model with the $S_3$ modular invariance in the framework of SU(5) GUT. The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $\tau$. The GUT…

Residual symmetry $G_\nu$ of neutrino mass matrix with a massless neutrino and embedding of $G_\nu$ and the residual symmetry $G_l$ of the charged lepton mass matrix into finite discrete groups $G$ is discussed. Massless neutrino results if…

Recent progress in the application of finite groups to neutrino mass matrices is reviewed, with special emphasis on the tetrahedral symmetry A_4.

We use modular symmetry as an organizing principle that attempts to simultaneously address the lepton flavor puzzle, inflation, and post-inflationary reheating. We demonstrate this approach using the finite modular group $A_4$ in the lepton…

We show how to realize two-zero textures of the Majorana neutrino mass matrix $M_\nu$ based on modular $A_4$ invariant models without flavons. In these models, all matter fields are assigned to three inequivalent singlets, ${\bf 1}$, ${\bf…

The leptonic Higgs doublet model of neutrino masses is implemented with an A_4 discrete symmetry (the even permutation of 4 objects or equivalently the symmetry of the tetrahedron) which has 4 irreducible representations: 1, 1', 1'', and 3.…

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…

We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…

We propose a non-holomorphic modular $A_4$ model under the assumption of universal couplings. In this framework, a charged lepton mass hierarchy is not created through parameter fine tuning or hierarchical Yukawa couplings, but instead is…

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…

For the algebra $I_n$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple weight and generalized weight (left and right) $I_n$-modules is given. It is proven that the category of…

Two sets of four 3x3 matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3 are constructed, forming two unitarily isomorphic reducible representations 3 of the group Z_2 x Z_2 called often the four-group. They are related…

The present work extends scotogenic and its modular $\mathcal{A}_4$ variation a step forward and demonstrates scotogenic modular $\mathcal{A}_4$ non-supersymmetric realization. To achieve this non-holomorphic modular symmetries come to…

We discuss type-II seesaw models adopting modular $A_4$ symmetry in supersymmetric framework. In our approach, the models are classified by the assignment of $A_4$ representations and modular weights for leptons and triplet Higgs fields.…

We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or from the seesaw. The constraint provided by modular invariance is so strong that neutrino mass ratios, lepton…

In this work, we have analyzed a neutrino model within the distinct framework of modular forms with degree, $ g>1 $ . This offers a more generalized scenario of modular forms which is popularly known as Siegel modular forms. We explore the…

We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or four-dimensional torus, they describe an equivalent class of a trio of the Einstein-Kahler forms (…

If and only if the small neutrino mixing sine s_13 is put zero, the effective neutrino mass matrix M with any mixing sines s_12 and s_23 is invariant under a cyclic group Z_2 of the order two and -- in the limit of m_2 - m_1 --> 0 -- also…

Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by…