Related papers: A note on generalized S-space-forms

We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface $S$ under deformation of the surface. Our calculations indicate that if…

We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…

We prove that it is consistent with large values of the continuum that there are no S-spaces. We also show that we can also have that compact separable spaces of countable tightness have cardinality at most the continuum.

We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal…

In a recent paper Ismail, Masson, and Suslov have established a continuous orthogonality relation and some other properties of a $_2\varphi_1$-Bessel function on a $q$-quadratic grid. Dick Askey suggested that the ``Bessel-type…

Let $G$ be a connected split reductive group over a finite field ${\mathbb F}_q$ and $X$ a smooth projective geometrically connected curve over ${\mathbb F}_q$. The $\ell$-adic cohomology of stacks of $G$-shtukas is a generalization of the…

We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.

Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…

We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…

$\mathbb{Z}_n$ S-folds of 5d SCFTs, including $T_N$, which lead to brane webs with $E_{6,7,8}$ 7-branes were discussed recently. We generalize the construction to `fractional quotients', which are based on $\mathbb{Z}_n$ actions linking…

We consider generalizations of classical function spaces by requiring that a holomorphic in ${\Omega}$ function satisfies some property when we approach from ${\Omega}$, not the whole boundary, but only a part of it. These spaces endowed…

We give a factorization of averages of Borcherds forms over CM points associated to a quadratic form of signature (n,2). As a consequence of this result, we are able to state a theorem like that of Gross and Zagier about which primes can…

A vector space partition $\mathcal{P}$ in $\mathbb{F}_q^v$ is a set of subspaces such that every $1$-dimensional subspace of $\mathbb{F}_q^v$ is contained in exactly one element of $\mathcal{P}$. Replacing "every point" by "every…

In this note we give a direct method to classify all stable forms on $\R^n$ as well as to determine their automorphism groups. We show that in dimension 6,7,8 stable forms coincide with non-degnerate forms. We present necessary conditions…

It has been known for some time that generalised geometry provides a particularly elegant rewriting of the action and symmetries of 10-dimensional supergravity theories, up to the lowest nontrivial order in fermions. By exhibiting the full…

By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian…

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital…

Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…

Let $G$ be a reductive group over a local field $F$ of characteristic zero, Archimedean or not. Let $X$ be a $G$-space. In this paper we study the existence of generalized Whittaker quotients for the space of Schwartz functions on $X$,…

Under the continuum hypothesis, there is a compact homogeneous strong S-space.