Related papers: The Capelli identity and Radon transform for Grass…

Let $f:X \to S$ be a Galois cover of Riemann surfaces, with Galois group $G$. In this paper we analyze the $G$-invariant divisors on $X$, and their associated spaces of meromorphic functions, differentials, and $q$-differentials. We…

We build compact moduli spaces of Grassmannian framed bundles over a Riemann surface, essentially replacing a group by its bi-invariant compactification. We do this both in the algebraic and symplectic settings, and prove a…

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian.…

We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of…

Here, we utilize facts about the big Chern classes discovered by M. Kapranov and independently by M. V. Nori to prove certain results about the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0. In…

In this work we are concerned with the multiplicity of the eigenvalues of the Neumann Laplacian in regions of Rn which are invariant under the natural action of a compact subgroup G of O(n). We give a partial positive answer (in the Neumann…

Our project is to define Radon-type transforms in symplectic geometry. The chosen framework consists of symplectic symmetric spaces whose canonical connection is of Ricci-type. They can be considered as symplectic analogues of the spaces of…

CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ``conformally invariant powers of the Laplacian'' via the Fefferman metric;…

We use localization method to understand the rational equivariant cohomology rings of real Grassmannians and oriented Grassmannians, then relate this to the Leray-Borel description which says the ring generators are equivariant Pontryagin…

We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference…

A $(K,\Lambda)$ shift-modulation invariant space is a subspace of $L^2(G)$, that is invariant by translations along elements in $K$ and modulations by elements in $\Lambda$. Here $G$ is a locally compact abelian group, and $K$ and $\Lambda$…

We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these…

In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the…

We reexamine the proofs of isospectrality of the counterexample domains to Kac' question `Can one hear the shape of a drum?' from an analytical viewpoint. We reformulate isospectrality in a more abstract setting as the existence of a…

Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If R has a grading similar to the case of Grassmann algebras,…

A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…

We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…

Using Gutzmer's formula, due to Lassalle, we characterise the image of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces.