We construct a categorification of the modular data associated with every family unipotent characters spetsial complex reflection group G ( d , 1 n ) . The construction category follows decomposition Fourier matrix as Kronecker tensor product exterior powers character table S cyclic order representations quantum universal enveloping algebra general linear Lie gl m parameter an even root unity 2...

The notion of B-spline based discrete differential forms is recalled and along with a Finite Element Hodge operator, it is used to design new numerical methods for solving the Vlasov-Poisson equations. Answer’s to the referees’ questions Aurore Back and Eric Sonnendrücker April 12, 2013 We thank the referees for the careful reading of our manuscript and for many interesting comments that helped...

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-...

We define the quantum exterior product ∧h and quantum exterior differential dh on Poisson manifolds. The quantum de Rham cohomology, which is a deformation quantization of the de Rham cohomology, is defined as the cohomology of dh. We also define the quantum Dolbeault cohomology. A version of quantum integral on symplectic manifolds is considered and the corresponding quantum Stokes theorem is ...

The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in R, and the scattering matrices in the exterior of the domains. Here, this link is extended to the study of the spectrum of the discrete Laplacian on finite graphs. For this purpose, two methods are devised for associating scattering matrices to the graphs. The Exterior -Int...

We recognise that Stegosaurus exhibited exterior chirality and could, therefore, have assumed either of two distinct, mirror-image forms. Our preliminary investigations suggest that both existed. Stegosaurus’s exterior chirality raises new questions such as the validity of well-known exhibits whilst offering new insights into long-standing questions such as the function of the plates. We inform...