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We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as: the sphere S2, the special orthogonal group SO(3), the positive definite ma...
where  is the reduction of . These results were subject to hypotheses on the local behavior of  at `, i.e., the restriction of  to a decomposition group at `, and to irreducibility hypotheses on...
In the absence of local lifting obstructions, the global obstruction lies in a Tate{Shafarevich group that can be analyzed via Tate duality. But we want more, namely to preserve local properties of ...
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary discrete series of the Virasoro algebra with 0 < c < 1.
We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A_infty functor from the representations up to homotopy of a Lie algebroid to those of its infin...
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the boo...
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of ...
We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe ...
We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log...
In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banac...
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness.
Matrices of locally analytic functions in two variables correspond to the maximal Cohen-Macaulay modules over plane curve singularities and to the local determinantal representations.
We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projecti...

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