Related papers: Singular BGG complexes over isotropic 2-Grassmanni…

The bisymplectic Grassmannian I$_2$Gr$(k, V)$ parametrizes k-dimensional subspaces of a vector space V which are isotropic with respect to two general skew-symmetric forms; it is a Fano variety which admits an action of a torus with a…

We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding…

We make the polynomial dependence on the fixed representation $\pi$ in our previous subconvex bound of $L(1/2,\pi \otimes \chi)$ for $\mathrm{GL}_2 \times \mathrm{GL}_1$ explicit, especially with respect to the usual conductor…

For two positive integers $m$ and $n$, we let ${\mathbb H}_n$ be the Siegel upper half plane of degree $n$ and let ${\mathbb C}^{(m,n)}$ be the set of all $m\times n$ complex matrices. In this article, we study differential operators on the…

Let $\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that…

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

We compute the {\Omega}^1(G) invariant when 1 {\to} H {\to} G {\to} K {\to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy…

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate a Grothendieck-Messing-Hodge-Tate…

We compute the Bieri-Neumann-Strebel invariants $\Sigma^1$ for the generalized solvable Baumslag-Solitar groups $\Gamma_n$ and their finite index subgroups. Using $\Sigma^1$, we show that certain finite index subgroups of $\Gamma_n$ cannot…

We construct a full exceptional collection of vector bundles in the derived category of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in a symplectic vector space of dimension $2n$ and in the derived category…

Invariant notions of a class of Segre varieties $\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a…

We outline, on a few instructive examples, the characteristic features of the approach to superbranes and super Born-Infeld theories based on the concept of partial spontaneous breaking of global supersymmetry (PBGS). The examples include…

Let $A/\overline{\mathbb{F}}\_p$ and $A'/\overline{\mathbb{F}}\_p$ be supersingular principally polarized abelian varieties of dimension $g>1$. For any prime $\ell \ne p$, we give an algorithm that finds a path $\phi \colon A \rightarrow…

There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…

We study the index theory of curved Bernstein-Gelfand-Gelfand (BGG) sequences in parabolic geometry and their role in $K$-homology and noncommutative geometry. The BGG-sequences fit into $K$-homology, and we solve their index problem. We…

We are interested in computing the Bredon cohomology with coefficients in the constant Mackey functor $\underline{ \mathbb{F}_2}$ for equivariant $\text{Rep}(C_2)$ spaces, in particular for Grassmannian manifolds of the form…

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and…

In this paper we construct resolutions of finite dimensional irreducible gl(m|n)-modules in terms of generalized Verma modules. The resolutions are determined by the Kostant cohomology groups and extend the strong…