Using the tensor product variety introduced in [6] and [7], the complete structure of the tensor product of a finite number of integrable highest weight modules of Uq(sl 2) is recovered. In particular, the elementary basis, Lusztig's canonical basis, and the basis adapted to the decomposition of the tensor product into simple modules are all exhibited as distinguished elements of certain spaces...

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction. AMS subject classification: 05E20, 05B25, 11T71, 94B25, 94B27, 51E22, 51E20, 20G40, 14L35

We give an algorithm for completing an order-m symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic results. If the centers of the product distribution are linearly independent, then we...

Let X a smooth quasi-projective algebraic surface, L a line bundle on X. Let X [n] the Hilbert scheme of n points on X and L the tautological bundle on X [n] naturally associated to the line bundle L on X. We explicitely compute the image Φ(L) of the tautological bundle L for the Bridgeland-King-Reid equivalence Φ : D(X ) → DbSn(X ), in terms of a complex C L of Snequivariant sheaves in DbSn(X ...

In this paper we study the properties of derivations of A B, where A and B are simple separable C*-algebras, and A B is the C*-completion of A B with respect to a C*-norm Yon A B and we will characterize the derivations of A B in terms of the derivations of A and B

We state a conjecture that relates the derived category of smooth representations $p$ -adic split reductive group with (quasi-)coherent sheaves on stack L-parameters. investigate in case principal block ${\rm GL}_n$ by showing functor should be given tensor product family interpolating modified Langlands correspondence over L-parameters is suggested work Helm and Emerton Helm.

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: “tensor product” and “multiplicity” varieties. These varieties are closely related to Nakajima’s quiver varieties and should play an important role in the geometric constructions of tensor products and intertwining operators. In particular it is shown that the s...

We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggest...

We explore the algebraic properties of a generalized version iterated-sums signature, inspired by previous work F. Király and H. Oberhauser. In particular, we show how to recover character property associated linear map on tensor algebra considering deformed quasi-shuffle product words. introduce three non-linear transformations signatures, close in spirit Machine Learning applications, some th...

Introduction 1 Acknowledgment 1 Notation 1 1. The tensor product with a motive of weight zero 3 1.1. The tensor product of two motives of weight zero 3 1.2. The tensor product of a torus with a motive of weight 0 3 1.3. The tensor product of an abelian scheme with a motive of weight 0 4 1.4. The tensor product of an extension of an abelian scheme by a torus with a motive of weight 0 4 2. The 1-...