Related papers: Modular forms and ellipsoidal T-designs
We define a notion of vexillar design for the flag variety in the spirit of the spherical designs introduced by Delsarte, Goethals and Seidel. For a finite subgroup of the orthogonal group, we explain how conditions on the group have the…
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs.…
The concept of spherical $t$-design, which is a finite subset of the unit sphere, was introduced by Delsarte-Goethals-Seidel (1977). The concept of Euclidean $t$-design, which is a two step generalization of spherical design in the sense…
We give an example of a one dimensional foliation $\cal F$ of degree two in a Zariski open set of a four dimensional weighted projective space which has only an enumerable set of algebraic leaves. These are defined over rational numbers and…
We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical $(k,k)$-designs and provide certain examples, including unit-norm tight frames, that attain these…
For any subset $Z \subseteq \mathbb{Q}$, consider the set $S_Z$ of subfields $L\subseteq \overline{\mathbb{Q}}$ which contain a co-infinite subset $C \subseteq L$ that is universally definable in $L$ such that $C \cap \mathbb{Q}=Z$. Placing…
By some SL(2, Z) modular forms introduced in [4] and [10], we construct some modular forms over SL2(Z) and some modular forms over {\Gamma}^0(2) and {\Gamma}_0(2) in odd dimensions. In parallel, we obtain some new cancellation formulas for…
For special $d$-dimensional hyperbolic shells $E$ with $ d\geq 5$ we show that the number of lattice points in $E$ intersected with a $d$-dimensional cube $C_r$ of edge length $r$, can be approximated by the volume of $E\cap C_r$, as $r$…
We extend to convenient finite quotients of a noetherian Lambda-module the classical result of K. Iwasawa giving the asymptotic expression of the l-part of the number of ideal class groups in Zl-extensions of number fields. Then, in the…
We consider lattices generated by finite Abelian groups. We prove that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if…
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…
We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
An integral lattice which is generated by some vectors of norm $q$ is called $q$-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices…
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for $n \in \{8, 24, 32, 48, 56, 72, 96\}$ every…
In De Simoi J., Kaloshin V., Wei Q. "Dynamical spectral rigidity among $\mathbb{Z}_2$-symmetric strictly convex domains close to a circle" (Appendix B coauthored with H. Hezari) Ann. of Math. 186.1 (2017), pp. 277-314 deformational spectral…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
By some SL(2, Z) modular forms introduced in [11] and [4] , we get some interesting anomaly cancellation formulas. As corollaries, we get some divisibility results of index of twisted Dirac operators.
Let W be a complex reflection group, acting on a complex vector space H. Kato has recently introduced the notion of a "Kostka system," which is a certain collection of finite-dimensional W-equivariant modules for the symmetric algebra on H.…
We provide a unique normal form for rank two irregular connections on the Riemann sphere.In fact, we provide a birational model where we introduce apparent singular points and where the bundlehas a fixed Birkhoff-Grothendieck decomposition.…